Results 1 to 10 of about 41 (41)
Etale and crystalline companions, I [PDF]
Épijournal de Géométrie Algébrique, 2022 Let $X$ be a smooth scheme over a finite field of characteristic $p$. Consider the coefficient objects of locally constant rank on $X$ in $\ell$-adic Weil cohomology: these are lisse Weil sheaves in \'etale cohomology when $\ell \neq p$, and ...
Kiran S. Kedlaya
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Group-theoretic Johnson classes and a non-hyperelliptic curve with torsion Ceresa class [PDF]
Épijournal de Géométrie Algébrique, 2023 Let l be a prime and G a pro-l group with torsion-free abelianization. We produce group-theoretic analogues of the Johnson/Morita cocycle for G -- in the case of surface groups, these cocycles appear to refine existing constructions when l=2.
Dean Bisogno +3 more
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Syntomic complexes and p-adic étale Tate twists
Forum of Mathematics, Pi, 2023 The primary goal of this paper is to identify syntomic complexes with the p-adic étale Tate twists of Geisser–Sato–Schneider on regular p-torsion-free schemes. Our methods apply naturally to a broader class of schemes that we call ‘F-smooth’.
Bhargav Bhatt, Akhil Mathew
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Forum of Mathematics, Pi, 2023 We define, for each quasisyntomic ring R (in the sense of Bhatt et al., Publ. Math. IHES 129 (2019), 199–310), a category $\mathrm {DM}^{\mathrm {adm}}(R)$ of admissible prismatic Dieudonné crystals over R and a functor from p-divisible groups ...
Johannes Anschütz +1 more
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Dieudonné theory via cohomology of classifying stacks
Forum of Mathematics, Sigma, 2021 We prove that if G is a finite flat group scheme of p-power rank over a perfect field of characteristic p, then the second crystalline cohomology of its classifying stack $H^2_{\text {crys}}(BG)$ recovers the Dieudonné module of G.
Shubhodip Mondal
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The equivalence of several conjectures on independence of $\ell$ [PDF]
Épijournal de Géométrie Algébrique, 2020 We consider several conjectures on the independence of $\ell$ of the \'etale cohomology of (singular, open) varieties over $\bar{\mathbf F}_p$. The main result is that independence of $\ell$ of the Betti numbers $h^i_{\text{c}}(X,\mathbf Q_\ell)$ for ...
Remy van Dobben de Bruyn
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A homotopy exact sequence for overconvergent isocrystals
Forum of Mathematics, Sigma, 2021 In this article we prove exactness of the homotopy sequence of overconvergent fundamental groups for a smooth and projective morphism in characteristic p. We do so by first proving a corresponding result for rigid analytic varieties in characteristic $0$,
Christopher Lazda, Ambrus Pál
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RAPOPORT–ZINK SPACES OF HODGE TYPE
Forum of Mathematics, Sigma, 2018 When $p>2$ , we construct a Hodge-type analogue of Rapoport–Zink spaces under the unramifiedness assumption, as formal schemes parametrizing ‘deformations’ (up to quasi-isogeny) of $p ...
WANSU KIM
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KAROUBI’S RELATIVE CHERN CHARACTER, THE RIGID SYNTOMIC REGULATOR, AND THE BLOCH–KATO EXPONENTIAL MAP
Forum of Mathematics, Sigma, 2014 We construct a variant of Karoubi’s relative Chern character for smooth separated schemes over the ring of integers in a $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le
GEORG TAMME
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$p$-DIVISIBILITY FOR COHERENT COHOMOLOGY
Forum of Mathematics, Sigma, 2015 We prove that the coherent cohomology of a proper morphism of noetherian schemes can be made arbitrarily $p$-divisible by passage to proper covers (for a fixed prime $p$).
BHARGAV BHATT
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