{"total":13,"items":[{"citing_arxiv_id":"2607.00088","ref_index":3,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Central isogenies and conjugacy classes in reductive groups","primary_cat":"math.RT","submitted_at":"2026-06-30T19:26:08+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Generalizes Steinberg's centralizer component description to unipotent elements under non-etale covers, with applications to L-parameter moduli multiplicities, deformation rings, and non-existence of Springer isomorphism for PGL_p in char p.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.25485","ref_index":262,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Prescribed lifts of 2-dimensional representations","primary_cat":"math.NT","submitted_at":"2026-06-24T07:13:50+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"Under standard Taylor-Wiles hypotheses, every irreducible 2-dimensional totally odd mod p Galois representation of the absolute Galois group of a totally real field F admits lifts on arbitrary prescribed components of local deformation rings, allowing potentially semistable conditions with arbitrary","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.06327","ref_index":5,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Arithmetic statistics of isogeny Selmer groups associated to hyperelliptic curves","primary_cat":"math.NT","submitted_at":"2026-06-04T16:01:13+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Asymptotic results for average sizes of isogeny Selmer groups of hyperelliptic Jacobians are obtained by combining Bhargava geometry-of-numbers with new Vinberg-theory parametrizations for Dynkin types B and C, plus lower bounds via Greenberg-Wiles.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.02799","ref_index":212,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"On the Schematic and Analytic Constructions of the Local Langlands Category","primary_cat":"math.NT","submitted_at":"2026-06-01T19:09:44+00:00","verdict":"UNVERDICTED","verdict_confidence":"UNKNOWN","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Constructs an equivalence for torsion coefficients between Zhu's category and Fargues-Scholze's category via Scholze's analytification functor and kimberlite theory, with applications to BunG decompositions and local Shimura varieties.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.10358","ref_index":110,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"On Galois categories and condensed contractible schemes","primary_cat":"math.AG","submitted_at":"2026-05-11T11:04:13+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"The condensed fundamental group of Spec(Z) is non-trivial, hence Spec(Z) is not condensed contractible.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.07843","ref_index":107,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Shape theory for condensed anima","primary_cat":"math.AT","submitted_at":"2026-05-08T15:07:57+00:00","verdict":"UNVERDICTED","verdict_confidence":"UNKNOWN","novelty_score":4.0,"formal_verification":"none","one_line_summary":"Shape theory for condensed anima recovers classical shape for paracompact compactly generated and locally contractible spaces while extending sheaf-condensed cohomology comparisons.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.04195","ref_index":25,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"A new perspective on the rank of Mazur's Eisenstein Hecke algebra","primary_cat":"math.NT","submitted_at":"2026-05-05T18:38:12+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"For primes N and p with N ≡ 1 mod p, the rank r of Mazur's Eisenstein Hecke algebra equals one plus the vanishing order of a mod-p zeta element interpolating L-values at -1 when r is 2 or 3, with a uniform extension to level N² and partial results for higher ranks.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"(23)ϕ T,χ(Y) =ϕ T,χ([δ] + [δ−1]−2) =ζ ps +ζ −1 ps −2. In particular (24)v(ϕ T,χ(Y)) = 2, sinceζ ps +ζ −1 ps −2 is a uniformizer for the degree 2 subfieldQ p(ζps +ζ −1 ps ) of the totally ramified fieldQ p(ζps) =Q p(χ). Proposition 5.8.We havev(ϕ T,χ(X))≥ 2 r , and equality holds ifh(0)∈ Z× p . Proof.Applyingϕ T,χ toF(X, Y), which maps to 0 inT, we see that (25) (ϕT,χ(X)) r =−((ζ ps+ζ −1 ps −2)h(ζps+ζ −1 ps −2)+ r−1X i=1 gai(ζps+ζ −1 ps −2)ϕT,χ(X) i). Sinceg ai(0)∈pZ p for all 1≤i≤r−1 by Corollary 5.6, it follows that ζps +ζ −1 ps −2 dividesg ai(ζps +ζ −1 ps −2) inZ p[ζps +ζ −1 ps ]. Therefore 2 = v(ζps +ζ −1 ps −2)≤v((ϕ T,χ(X)) r) =rv(ϕ T,χ(X)), which proves the inequality. Now suppose thath(0)∈Z × p . To show that equality holds, it suffices to"},{"citing_arxiv_id":"2605.03108","ref_index":134,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Gaiotto Loci and the Nilpotent Cone for $\\mathrm{Sp}_{2n}(\\mathbb C)$","primary_cat":"math.AG","submitted_at":"2026-05-04T19:48:35+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"For the standard representation of Sp_{2n}(C), the Gaiotto locus is the Bialynicki-Birula closure associated to U(Sp_{2n-2}(C)) inside the nilpotent cone, and its intersection with the stable cotangent chart is the closure of the conormal bundle to the one-spinor stratum of the generalized theta-div","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.02763","ref_index":139,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Birational invariance of higher Amitsur groups","primary_cat":"math.AG","submitted_at":"2026-05-04T16:03:27+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"The nth Amitsur group is a stable G-birational invariant of smooth projective G-varieties over char-0 fields for all n≥2.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.00766","ref_index":83,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Supersingular reduction and strongly special intersections in powers of the modular curve","primary_cat":"math.NT","submitted_at":"2026-05-01T16:26:57+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Assuming Lang-Trotter-type sparsity for simultaneous supersingular reductions, the paper proves two Zilber-Pink-type finiteness results for Hodge generic curves in Y(1)^n via André's G-function method.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.00759","ref_index":82,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Lang-Trotter phenomena and unlikely intersections","primary_cat":"math.NT","submitted_at":"2026-05-01T16:18:46+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Lang-Trotter conjecture for elliptic curve pairs implies new Zilber-Pink cases for curves in A_3 via André's G-functions method, without boundary intersection assumptions.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.25842","ref_index":3,"ref_count":2,"confidence":0.88,"is_internal_anchor":false,"paper_title":"The coordinate ring of the universal centralizer via Demazure operators","primary_cat":"math.RT","submitted_at":"2026-04-28T16:47:15+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"The coordinate ring of the universal centralizer equals the result of applying Demazure operators to the coordinate ring of X precisely when the W-fixed points of the Weil restriction of X is an integral scheme.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.18099","ref_index":56,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Solvable Descent and the Grunwald Problem for Solvable Groups","primary_cat":"math.NT","submitted_at":"2026-04-20T11:16:37+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"A new fibration theorem implies solvable descent, solving the Grunwald problem for solvable groups up to the Brauer-Manin obstruction.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null}],"limit":50,"offset":0}