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Descent for solid quasi-coherent sheaves on perfectoid spaces

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arxiv 2403.01951 v2 pith:LBRJ2FIV submitted 2024-03-04 math.AG math.NT

Johannes Anschütz , Lucas Mann This is my paper · ORCID
classification math.AGmath.NT
keywords quasi-coherentsheavessoliddescentperfectoidspacescurvesdevelopment
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abstract

We prove $v$-descent for solid quasi-coherent sheaves on perfectoid spaces as a key technical input for the development of a $6$-functor formalism with values in solid quasi-coherent sheaves on relative Fargues--Fontaine curves.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Localizing invariants of inverse limits

    math.KT 2025-02 conditional novelty 8.0 of 10

    Continuous K-theory of nuclear modules on Spf(R^hat_I) is isomorphic to lim_n K(R/I^n), via internal projectivity and strongly Mittag-Leffler inverse sequences.

  2. A 6-functor formalism for solid quasi-coherent sheaves on the Fargues-Fontaine curve

    math.AG 2024-12 accept novelty 7.0 of 10

    A 6-functor formalism for Z_p-linear solid quasi-coherent sheaves on small v-stacks is constructed, yielding Poincare duality for pro-etale Q_p-cohomology.

  3. Reconstruction of Formal Schemes from Categories of Nuclear Modules

    math.AG 2026-07 accept novelty 6.5 of 10

    Formal schemes X are reconstructed from Nuc^Ef(X) or Nuc^CS(X) by recovering D_tors(X) as the maximal strongly compactly generated localizing tensor ideal and taking its Balmer spectrum.

  4. An axiomatic approach to analytic $1$-affineness

    math.AG 2025-09 conditional novelty 6.0 of 10

    An axiomatic framework proves 1-affineness for analytic Betti stacks, analytic de Rham stacks, and rigid analytic varieties, giving categorical Künneth formulas.

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