Fourier transforms and $p$-adic ‘Weil II’

By Kiran S. Kedlaya. Compositio Mathematica, 2002

82 citations recorded by the source corpus.

We give a purity theorem in the manner of Deligne's ‘Weil II’ theorem for rigid cohomology with coefficients in an overconvergent $F$-isocrystal; the proof mostly follows Laumon's Fourier-theoretic approach, transposed into the setting of arithmetic $\mathcal{D}$-modules. This yields in particular a complete, purely $p$-adic proof of the Weil conjectures when combined with recent results on $p$-adic differential equations by André, Christol, Crew, Kedlaya, Matsuda, Mebkhout and Tsuzuki.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/289d9cd446ec4f2f951b3214bfb2be39d2060f09

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Slope filtrations revisited (2005, methodology): “Many of these are in the study of rigid p-adic cohomology of varieties over fields of characteristic p: these include a full faithfulness theorem for restriction between the categories of overconvergent and convergent F -isocrystals [20], a finiteness theorem with coefficients [22], and an analogue ”
Slope filtrations for relative Frobenius (2006, background): “local monodromy theorem, originally conjectured by Crew [13]; this analogue can be used to establish various structural results such as ﬁniteness of cohomology [23] and purity in the sense of Deligne [24]. The eﬀect of the slope ﬁltration theorem on p-adic Hodge theory has perhaps been even more acu”