Chromatic Higher Semiadditivity by Height Induction

Shay Ben-Moshe

REVIEW 3 major objections 4 minor 23 references

Chromatic Higher Semiadditivity by Height Induction

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper gives a new proof that the category of $K(n)$-local spectra is $\infty$-semiadditive, by induction on chromatic height through algebraic $K$-theory, redshift, and the chromatic nullstellensatz rather than the Ravenel–Wilson…

desk verdict A fresh induction proof of a known theorem that is likely right and worth refereeing, but the load-bearing map in Proposition 3.18 needs a precise citation. read the letter →

arxiv 2501.08092 v1 pith:KRR7B2VN submitted 2025-01-14 math.AT math.KT

Shay Ben-Moshe This is my paper · ORCID

classification math.ATmath.KT MSC 55P4219D99

keywords highersemiadditivitychromatichomotopytheoryMoravaK-theoryalgebraicredshiftnullstellensatzLubin-Tatespectraπ-finitespaces

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proves that the category $\mathrm{Sp}_{K(n)}$ of $K(n)$-local spectra is $\infty$-semiadditive: for every $\pi$-finite space $A$, the norm map $\operatorname{colim}_A X \to \lim_A X$ is an equivalence for every diagram $X$. The proof is organized as an induction on chromatic height $n$, and the inductive step runs through $T(n+1)$-localized algebraic $K$-theory and $n$-monochromatic categories. Redshift and the chromatic nullstellensatz then transfer the structure to the module category of a height-$(n+1)$ Lubin–Tate spectrum, where higher semiadditivity is detected. This replaces the Ravenel–Wilson computation of the Morava $K$-theory of Eilenberg–MacLane spaces, which carried the original Hopkins–Lurie proof, with structural facts about algebraic $K$-theory. If the proof is correct, the deepest known symmetry of chromatic homotopy theory is not an isolated calculation but follows from a transfer principle at each height.

What carries the argument

The load-bearing mechanism is the composite of three objects: $\mathrm{Cat}_{M_n}$, the category of $n$-monochromatic categories, whose $\infty$-semiadditivity follows from the induction hypothesis; $K_{T(n+1)}$, the lax symmetric monoidal functor given by $T(n+1)$-localized algebraic $K$-theory, which factors through $\mathrm{Cat}_{M_n}$ by purity and preserves constant $\pi$-finite $p$-space colimits by a descent argument; and the ring map $K_{T(n+1)}(S_{K(n)}) \to E_{n+1}(\kappa)$ supplied by redshift and the chromatic nullstellensatz. Harpaz’s characterization of higher semiadditivity, in which a symmetric monoidal category is higher semiadditive exactly when there is a symmetric monoidal functor from the category $\mathrm{Span}(S^{\pi\text{-fin}})$ of spans of $\pi$-finite spaces to it, converts this composite into the $p$-typical $\infty$-semiadditivity of $\mathrm{Mod}_{E_{n+1}(\kappa)}$.

What would settle it

Find a $\pi$-finite $p$-space $A$, for instance $B^m C_p$ for some $m$, and a height $n$ for which the cardinality $|A|_{S_{K(n)}}$ vanishes in $\pi_0$ of the $K(n)$-local sphere; equivalently, exhibit a constant diagram on the unit whose norm map is not an equivalence, which would directly contradict Theorem 3.19. A narrower check on the proof is to verify Proposition 3.18 at $n=1$, tracing whether the ring map $K_{T(2)}(S_{K(1)}) \to E_2(\kappa)$ really induces a symmetric monoidal base change on module categories; a failure there would break the inductive bridge at the first step.

Watch

Extended reading notes

Core claim

Theorem 3.19 asserts that $\mathrm{Sp}_{K(n)}$ is $\infty$-semiadditive for every height $n$. The new content is the mechanism: assuming $\infty$-semiadditivity at height $n$, the category $\mathrm{Cat}_{M_n}$ of $n$-monochromatic categories is $\infty$-semiadditive; the $T(n+1)$-localized algebraic $K$-theory functor $K_{T(n+1)}\colon \mathrm{Cat}_{M_n} \to \mathrm{Sp}_{T(n+1)}$ is lax symmetric monoidal and preserves constant $\pi$-finite $p$-space colimits; this produces a strong symmetric monoidal functor $\mathrm{Span}(S^{p\text{-fin}}) \to \mathrm{Mod}_{K_{T(n+1)}(S_{K(n)})}$; and redshift together with the chromatic nullstellensatz supplies a commutative ring map $K_{T(n+1)}(S_{K(n)}) \to E_{n+1}(\kappa)$ for an algebraically closed field $\kappa$ of characteristic $p$. Base change along that map makes $\mathrm{Mod}_{E_{n+1}(\kappa)}$ $p$-typically $\infty$-semiadditive, and the Hopkins–Lurie thick-subcategory argument lifts this to all of $\mathrm{Sp}_{K(n+1)}$. The paper therefore reaches the original conclusion by a route that does not use the Ravenel–Wilson calculation.

Load-bearing premise

The load-bearing premise is that redshift and the chromatic nullstellensatz really do provide a commutative ring map from the $T(n+1)$-localized algebraic $K$-theory of the $K(n)$-local sphere to a height-$(n+1)$ Lubin–Tate spectrum, and that base change along this map transfers the higher commutative structure to $E_{n+1}(\kappa)$-modules; if that map did not exist or failed to be symmetric monoidal, the induction could not cross from height $n$ to height $n+1$.

Editorial extensions

If this is right

For every $n$ and every $\pi$-finite space $A$, the norm map $\operatorname{colim}_A X \to \lim_A X$ is an equivalence for all diagrams $X$ in $\mathrm{Sp}_{K(n)}$, so over such shapes finite colimits and limits coincide in the $K(n)$-local category.
The proof supplies a uniform inductive bridge from height $n$ to height $n+1$ through $T(n+1)$-localized $K$-theory, so the entire tower of heights rests on the height-$0$ and height-$1$ bases together with redshift and the chromatic nullstellensatz.
The Ravenel–Wilson computation of Morava $K$-theory of Eilenberg–MacLane spaces is not needed; the height-$1$ base can be handled by the Anderson–Hodgkin computation or by a short cardinality argument.
The proof identifies $\mathrm{Mod}_{E_{n+1}(\kappa)}$ as the category through which higher semiadditivity is inherited, giving a new direct link between algebraic $K$-theory redshift and ambidexterity in chromatic homotopy theory.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A likely extension, not pursued in the paper, is to replace the $K(n)$-local sphere by the telescopic $T(n)$-local sphere in the same induction; the author explicitly asks this as Question 1.1, and the transfer step in Proposition 3.18 is the place where such an extension would succeed or fail.
The proof suggests a redshift principle for higher semiadditivity: $T(n+1)$-localized algebraic $K$-theory raises the semiadditive height by one, so one could test whether other localizations, truncations, or module categories carry analogous transferred structures.
A testable strengthening would be to show that every Lubin–Tate spectrum $E_n$ over a perfect residue field, not only the algebraically closed field supplied by the nullstellensatz, supports the $\infty$-semiadditivity transfer; Proposition 3.18 proves it for one such field, and the general case would make the statement canonical.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The new thing here is the route, not the theorem: ∞-semiadditivity of Sp_K(n) was already proved by Hopkins–Lurie and generalized by Carmeli–Schlank–Yanovski. The author gives an induction on chromatic height that replaces the Ravenel–Wilson computation with algebraic K-theory, redshift, and the chromatic nullstellensatz. If the proof checks out, it is a genuine methodological step, showing that a long computational input can be swapped for structural tools.

What the paper does well: the base case n=1 is handled cleanly, and the paper explicitly notices and avoids a circular use of the theorem in an earlier joint work. The assumptions are stated, the induction is honest, and the author acknowledges that Mathew independently had a similar idea. The proof outline is coherent, and the theorem being already known means the risk to the mathematical literature is low.

The biggest soft spot is Proposition 3.18. The proof is one sentence: “By redshift and the chromatic nullstellensatz [Yua24, BSY24], we have a map K_T(n+1)(S_K(n)) → E_{n+1}(κ) in CAlg(Sp_T(n+1)).” The direction, the E_∞ ring structure, and the choice of κ are all load-bearing. Neither citation comes with a theorem number or a derivation, so a referee cannot verify that the asserted map is exactly what those papers produce. I do not think this is fatal—the cited results plausibly give exactly this—but it is the kind of gap that should be closed before publication. Proposition 3.4, the p-typical version of Harpaz’s characterization, is stated without proof; it is likely formal but needs a reference or a short argument. The proof of Proposition 3.14 also has minor typos in the diagram (missing parentheses) that should be fixed, though the mathematics there looks standard.

I cannot independently verify the full chain of deep external results, but the internal logic is coherent, the author is careful about circularity, and the theorem is known, so the stakes are manageable.

This paper is for chromatic homotopy theorists and people working on higher semiadditivity. It deserves a serious referee: the new proof is interesting and likely correct, and a referee can focus the author on tightening the citations and filling the two gaps. I would send it to peer review, expecting major revision on the presentation of those black boxes.

Referee Report

3 major / 4 minor

Summary. The paper gives a new proof of the ∞-semiadditivity of the K(n)-local stable homotopy category, proceeding by induction on the chromatic height. The base case n=1 is proved in Proposition 2.2 using known cardinality computations for KU_p. For the inductive step, Assumption 3.15 posits ∞-semiadditivity of Sp_K(n); Proposition 3.8 then deduces ∞-semiadditivity of the category Cat_{M_n} of n-monochromatic categories. Building on a variant of the higher descent theorem (Proposition 3.14), the paper constructs a strong symmetric monoidal, π-finite p-space colimit–preserving functor from Span(Sp-fin) to modules over K_{T(n+1)}(S_K(n)) (Lemma 3.16 and Proposition 3.17). Proposition 3.18 post-composes with a base change along an E_∞ ring map K_{T(n+1)}(S_K(n)) → E_{n+1}(κ), which is asserted to follow from redshift and the chromatic nullstellensatz. The paper then concludes, via the Hopkins–Lurie thick subcategory argument (Theorem 3.19), that Sp_K(n+1) is ∞-semiadditive.

Significance. If the proof is correct, it provides a substantial conceptual simplification of the ∞-semiadditivity of K(n)-local spectra, avoiding the Ravenel–Wilson computation entirely and instead using algebraic K-theory, redshift, and the chromatic nullstellensatz. The induction is honest: the height-n case is assumed only for the previous height, and the base height 1 is proved separately. The paper also explicitly identifies and sidesteps a circular argument in [BMCSY24b] regarding Proposition 2.1, which is a strength. The overall strategy is plausible and the formal reductions are clearly presented. However, the proof leans heavily on external results, and two load-bearing steps are not justified with sufficient precision, as detailed in the major comments.

major comments (3)

[§3.4 (Lemma 3.16 and Proposition 3.17)] The proof of the colimit-preservation of the functor Sp-fin → Mod_{K_{T(n+1)}(S_K(n))} invokes Proposition 3.14, which is stated for categories in Cat_{L^f_n}. However, the functor is applied to objects of the form Mn[A] in Cat_{M_n}, and Definition 3.7 defines Cat_{M_n} using L_n-locality and L_{n-1}-acyclicity, not telescopic L^f_n-locality. The footnote in Definition 3.7 explicitly notes that the cited literature [BMCSY24b] used the telescopic variant of 'n-monochromatic'. The paper does not prove that Cat_{M_n} ⊆ Cat_{L^f_n} or that the higher descent theorem holds for the L_n-based monochromatic categories as defined here. Since this is exactly what turns the lax symmetric monoidal functor into a strong symmetric monoidal colimit-preserving functor, the gap is load-bearing for the induction.
[§3.4 (Proposition 3.18)] The existence of an E_∞ ring map K_{T(n+1)}(S_K(n)) → E_{n+1}(κ) in CAlg(Sp_{T(n+1)}) is asserted in a single sentence with only the vague citations '[Yua24, BSY24]'. The base change functor to Mod_{E_{n+1}(κ)}—and hence the entire transfer of p-typical higher semiadditivity to Mod_{E_{n+1}(κ)}—depends on this being a map of commutative algebras that is nonzero and defined in Sp_{T(n+1)}. The paper should state the precise theorem from the cited works that yields this map, indicate how the redshift and chromatic nullstellensatz hypotheses are met, and confirm that the map is indeed an E_∞ ring map rather than merely a nonzero map of spectra. Without this, the induction from height n to height n+1 fails precisely at the point where the new machinery is invoked.
[§3.4 (proof of Theorem 3.19)] The final thick subcategory argument uses that the completed Johnson–Wilson spectrum \hat E(n+1) is a retract of E_{n+1}(κ) and that all dualizable K(n+1)-local spectra lie in the thick subcategory generated by \hat E(n+1), citing [HS99, Theorem 8.9]. This is a standard input, but the paper should make explicit that the field κ is chosen so that this retract exists (e.g., κ algebraically closed of characteristic p ensures the appropriate Lubin–Tate spectrum is a retract of E_{n+1}(κ)); as written, the sentence 'the completed Johnson–Wilson spectrum \hat E(n+1) is a retract of E_{n+1}(κ)' is stated without justification or a reference.

minor comments (4)

[§3.3 (proof of Proposition 3.14)] In the second commutative diagram, the bottom-right term is written 'KT(n+1)(R[Ω colim∆op A•)' and is missing a closing parenthesis; it should be 'KT(n+1)(R[Ω colim∆op A•])'.
[§3.4 (Lemma 3.16 and Proposition 3.17)] The notation 'dMod_{K_{T(n+1)}(S_K(n))}' appears in several places; this is likely a typo for '[Mod_{K_{T(n+1)}(S_K(n))}', the category of modules. The same symbol appears in Proposition 3.18 and should be corrected.
[§3.2 (proof of Proposition 3.8)] The sentence 'the right adjoint of g!, namely g*, is itself left adjoint to g*' is tautological as written; presumably the intended meaning is that g* is left adjoint to g_* (or similar), and the statement should be clarified.
[§2 (proof of Proposition 2.2)] The notation '|C_p|_{KU_p}' is used without defining the cardinality of a finite group in a semiadditive category; a brief reference to [CSY22, §3.3] would improve readability for readers not familiar with this notation.

Circularity Check

0 steps flagged · score 2.0 of 10

Honest height induction with external redshift/nullstellensatz input; no construction-level circularity found.

full rationale

The derivation is an honest induction and does not reduce to its inputs. The main claim, Theorem 3.19, assumes Sp_K(n) is ∞-semiadditive (Assumption 3.15) and proves Sp_K(n+1); the base case is handled separately in Proposition 2.2 via [CSY22, Cor. 3.3.10] and [CSY21, Thm. 3.2.7]. The one place where a circularity might have occurred is explicitly identified and repaired: Proposition 2.1 is flagged as relying on the target result in [BMCSY24b] ('which would put us in a circular situation') and is re-derived from Anderson–Hodgkin. Proposition 3.14 is likewise re-proved 'with slight modifications to avoid higher semiadditivity assumptions.' The transfer step Proposition 3.18 invokes a map K_{T(n+1)}(S_K(n)) → E_{n+1}(κ) from redshift and the chromatic nullstellensatz [Yua24, BSY24]; this is a load-bearing external input and is cited without a theorem number, so it deserves verification, but nothing in the paper defines that map in terms of the conclusion or fits it to the semiadditivity being proved. Self-citations to [BMCSY24b, BMS24, BM24] are frequent, but the relevant results are either conditional on the inductive hypothesis and proved by sketch (Proposition 3.8), or re-derived in the text (Proposition 3.14), so they are not unverified loads that force the conclusion. The final norm equivalence follows from Hopkins–Lurie's thick subcategory argument and [HS99, Thm. 8.9]. Overall the central claim has independent content; the cited group's prior work is used as a tool, not as a self-fulfilling premise.

Assumptions & free parameters 0 free parameters · 7 assumptions · 0 invented entities

The proof introduces no fitted parameters and no new entities. Its central claim rests on a web of external theorems from chromatic K-theory and ∞-category theory, listed above. The most delicate input is the redshift/nullstellensatz map, which is not reproved here.

assumptions (7)

domain assumption The ∞-category Pr^L of presentable categories is ∞-semiadditive
Used in Proposition 3.8 to build a Span(S^{π-fin}) -> Pr^L functor; cited to [HL13, Example 4.3.11] and [BM24, Proposition 2.21].
domain assumption T(n+1)-localized algebraic K-theory preserves sifted colimits for n ≥ 1
Used in Proposition 3.14 to pass sifted colimits through KT(n+1); from [LMMT24, Corollary 4.32]. The restriction n ≥ 1 is discussed in Section 2.
domain assumption Purity and vanishing theorems for T(n+1)-localized K-theory of L_n-local categories
Used in Propositions 3.10 and 3.12 to identify KT(n+1) on monochromatic categories and on L_nS with KT(n+1)(S_K(n)); from [CMNN24, Theorem C] and [LMMT24, Purity Theorem].
domain assumption Redshift and the chromatic nullstellensatz produce a commutative ring map KT(n+1)(S_K(n)) -> E_{n+1}(κ)
Load-bearing in Proposition 3.18; from [Yua24] and [BSY24]. This is the input that carries the higher semiadditive structure to Lubin-Tate modules.
domain assumption Sp_K(n+1) is 1-semiadditive
Assumed at the start of Section 1.2 and used in the descent/purity input and in the Hopkins-Lurie induction; cited to [CM17].
domain assumption p-typical analogue of Harpaz's universal characterization of higher semiadditivity (Proposition 3.4)
Stated in Section 3.1 with the indication that the same proofs as [Har20, Corollary 5.9] apply; used to convert a Span(S_p-fin)-preserving functor into p-typical ∞-semiadditivity.
domain assumption All dualizable K(n+1)-local spectra lie in the thick subcategory generated by the completed Johnson-Wilson spectrum
Used at the end of Theorem 3.19 to propagate the norm isomorphism from E_{n+1}(κ) to S_K(n+1); from [HS99, Theorem 8.9].

how reviews work

0 comments

Cite this review

Pith. "Pith review of Chromatic Higher Semiadditivity by Height Induction." pith.science (2026). https://pith.science/paper/KRR7B2VN

@misc{pith2026250108092,
  author       = {Pith},
  title        = {Pith review of: Chromatic Higher Semiadditivity by Height Induction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KRR7B2VN}},
  note         = {Machine review of arXiv:2501.08092}
}

abstract

We give a new proof of the $\infty$-semiadditivity of $K(n)$-local spectra. The proof proceeds by induction on the height via algebraic K-theory, utilizing recent advances in chromatic homotopy theory and the redshift conjecture, instead of using the Ravenel-Wilson computation of the Morava K-theory of Eilenberg-MacLane spaces.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

23 extracted references · 22 canonical work pages

[1]

Anderson and Luke Hodgkin

D.W. Anderson and Luke Hodgkin. The K-theory of Eilenberg-Maclane complexes . Topology , 7(3):317--329, 1968

work page 1968
[2]

Categorical Ambidexterity

Shay Ben-Moshe. Categorical Ambidexterity . 2024. arXiv:2411.17281v1 https://arxiv.org/abs/2411.17281v1 [math.CT]

work page arXiv 2024
[3]

Schlank, and Lior Yanovski

Shay Ben-Moshe, Shachar Carmeli, Tomer M. Schlank, and Lior Yanovski. Chromatic Cardinalities via Redshift . International Mathematics Research Notices , 2024(14):10918--10924, 05 2024

work page 2024
[4]

Schlank, and Lior Yanovski

Shay Ben-Moshe, Shachar Carmeli, Tomer M. Schlank, and Lior Yanovski. Descent and Cyclotomic Redshift for Chromatically Localized Algebraic K -theory . Journal of the American Mathematical Society , 2024

work page 2024
[5]

Shay Ben-Moshe and Tomer M. Schlank. Higher semiadditive algebraic K-theory and redshift . Compositio Mathematica , 160(2):237--287, 2024

work page 2024
[6]

Schlank, and Allen Yuan

Robert Burklund, Tomer M. Schlank, and Allen Yuan. The Chromatic Nullstellensatz . Annals of Mathematics , 2024

work page 2024
[7]

Characters and transfer maps via categorified traces

Shachar Carmeli, Bastiaan Cnossen, Maxime Ramzi, and Lior Yanovski. Characters and transfer maps via categorified traces . 2022. arXiv:2210.17364v2 https://arxiv.org/abs/2210.17364v2 [math.AT]

arXiv 2022
[8]

A short proof of telescopic Tate vanishing

Dustin Clausen and Akhil Mathew. A short proof of telescopic Tate vanishing . Proceedings of the American Mathematical Society , 145(12):5413--5417, 2017

work page 2017

Show all 23 references

[9]

Descent and vanishing in chromatic algebraic K -theory via group actions

Dustin Clausen, Akhil Mathew, Niko Naumann, and Justin Noel. Descent and vanishing in chromatic algebraic K -theory via group actions . Annales scientifiques de l'\'Ecole normale sup\'erieure , 57(4):1135--1190, 2024

2024
[10]

Schlank, and Lior Yanovski

Shachar Carmeli, Tomer M. Schlank, and Lior Yanovski. Ambidexterity and Height . Advances in Mathematics , 385:107763, 2021

2021
[11]

Schlank, and Lior Yanovski

Shachar Carmeli, Tomer M. Schlank, and Lior Yanovski. Ambidexterity in chromatic homotopy theory . Inventiones mathematicae , 228(3):1145–1254, 2022

2022
[12]

Higher semiadditive Grothendieck-Witt theory and the K(1) -local sphere

Shachar Carmeli and Allen Yuan. Higher semiadditive Grothendieck-Witt theory and the K(1) -local sphere . Communications of the American Mathematical Society , 3(02):65--111, 2023

2023
[13]

The Tate spectrum of v_n -periodic complex oriented theories

John PC Greenlees and Hal Sadofsky. The Tate spectrum of v_n -periodic complex oriented theories . Mathematische Zeitschrift , 222(3):391--406, 1996

1996
[14]

Ambidexterity and the universality of finite spans

Yonatan Harpaz. Ambidexterity and the universality of finite spans . Proceedings of the London Mathematical Society , 121(5):1121--1170, 2020

2020
[15]

Dwyer--Kan localization revisited

Vladimir Hinich. Dwyer--Kan localization revisited . Homology, Homotopy and Applications , 18(1):27--48, 2016

2016
[16]

Ambidexterity in K(n) -Local Stable Homotopy Theory

Michael Hopkins and Jacob Lurie. Ambidexterity in K(n) -Local Stable Homotopy Theory . https://www.math.ias.edu/ lurie/papers/Ambidexterity.pdf, 2013

2013
[17]

Tate cohomology lowers chromatic Bousfield classes

Mark Hovey and Hal Sadofsky. Tate cohomology lowers chromatic Bousfield classes . Proceedings of the American Mathematical Society , 124(11):3579--3585, 1996

1996
[18]

Morava K -theories and localisation , volume 666

Mark Hovey and Neil P Strickland. Morava K -theories and localisation , volume 666. American Mathematical Soc., 1999

1999
[19]

Tate cohomology and periodic localization of polynomial functors

Nicholas J Kuhn. Tate cohomology and periodic localization of polynomial functors . Inventiones mathematicae , 157(2):345--370, 2004

2004
[20]

Purity in chromatically localized algebraic K -theory

Markus Land, Akhil Mathew, Lennart Meier, and Georg Tamme. Purity in chromatically localized algebraic K -theory . Journal of the American Mathematical Society , 37:1011--1040, 2024

2024
[21]

Ravenel and W

Douglas C. Ravenel and W. Stephen Wilson. The Morava K-Theories of Eilenberg-MacLane Spaces and the Conner-Floyd Conjecture . American Journal of Mathematics , 102(4):691--748, 1980

1980
[22]

Stable model categories are categories of modules

Stefan Schwede and Brooke Shipley. Stable model categories are categories of modules . Topology , 42(1):103--153, 2003

2003
[23]

Examples of chromatic redshift in algebraic K -theory

Allen Yuan. Examples of chromatic redshift in algebraic K -theory . Journal of the European Mathematical Society , 2024

2024

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

Anderson and Luke Hodgkin

D.W. Anderson and Luke Hodgkin. The K-theory of Eilenberg-Maclane complexes . Topology , 7(3):317--329, 1968

work page 1968

[2] [2]

Categorical Ambidexterity

Shay Ben-Moshe. Categorical Ambidexterity . 2024. arXiv:2411.17281v1 https://arxiv.org/abs/2411.17281v1 [math.CT]

work page arXiv 2024

[3] [3]

Schlank, and Lior Yanovski

Shay Ben-Moshe, Shachar Carmeli, Tomer M. Schlank, and Lior Yanovski. Chromatic Cardinalities via Redshift . International Mathematics Research Notices , 2024(14):10918--10924, 05 2024

work page 2024

[4] [4]

Schlank, and Lior Yanovski

Shay Ben-Moshe, Shachar Carmeli, Tomer M. Schlank, and Lior Yanovski. Descent and Cyclotomic Redshift for Chromatically Localized Algebraic K -theory . Journal of the American Mathematical Society , 2024

work page 2024

[5] [5]

Shay Ben-Moshe and Tomer M. Schlank. Higher semiadditive algebraic K-theory and redshift . Compositio Mathematica , 160(2):237--287, 2024

work page 2024

[6] [6]

Schlank, and Allen Yuan

Robert Burklund, Tomer M. Schlank, and Allen Yuan. The Chromatic Nullstellensatz . Annals of Mathematics , 2024

work page 2024

[7] [7]

Characters and transfer maps via categorified traces

Shachar Carmeli, Bastiaan Cnossen, Maxime Ramzi, and Lior Yanovski. Characters and transfer maps via categorified traces . 2022. arXiv:2210.17364v2 https://arxiv.org/abs/2210.17364v2 [math.AT]

arXiv 2022

[8] [8]

A short proof of telescopic Tate vanishing

Dustin Clausen and Akhil Mathew. A short proof of telescopic Tate vanishing . Proceedings of the American Mathematical Society , 145(12):5413--5417, 2017

work page 2017