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15 July 2006 Finiteness of rigid cohomology with coefficients
Kiran S. Kedlaya
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Duke Math. J. 134(1): 15-97 (15 July 2006). DOI: 10.1215/S0012-7094-06-13412-9

Abstract

We prove that for any field k of characteristic p>0, any separated scheme X of finite type over k, and any overconvergent F-isocrystal E over X, the rigid cohomology Hrigi(X,E) and rigid cohomology with compact supports Hc,rigi(X,E) are finite-dimensional vector spaces over an appropriate p-adic field. We also establish Poincaré duality and the Künneth formula with coefficients. The arguments use a pushforward construction in relative dimension 1, based on a relative version of Crew's [Cr] conjecture on the quasi-unipotence of certain p-adic differential equations

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Kiran S. Kedlaya. "Finiteness of rigid cohomology with coefficients." Duke Math. J. 134 (1) 15 - 97, 15 July 2006. https://doi.org/10.1215/S0012-7094-06-13412-9

Information

Published: 15 July 2006
First available in Project Euclid: 4 July 2006

zbMATH: 1133.14019
MathSciNet: MR2239343
Digital Object Identifier: 10.1215/S0012-7094-06-13412-9

Subjects:
Primary: 14F30

Rights: Copyright © 2006 Duke University Press

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Vol.134 • No. 1 • 15 July 2006
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