Finiteness of rigid cohomology with coefficients
By Kiran S. Kedlaya. 2002
91 citations recorded by the source corpus.
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 H^i(X, E) and rigid cohomology with compact supports H^i_c(X,E) are finite dimensional vector spaces. We also establish Poincare duality and the Kunneth formula with coefficients. The arguments use a pushforward construction in relative dimension 1, based on a relative version of Crew's conjecture on the quasi-unipotence of certain p-adic differential equations.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/0c9bc5aef473a9578bd07e330a5d0f9dbf9e77c1
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In Applied Mathematics
In Geometry and Topology
- Kiran S. Kedlaya
- Ruochuan Liu
- Peter Scholze
- Alan G. B. Lauder
- T. Mochizuki
- Jonathan Pottharst
- Tomoyuki Abe
- David Lubicz
In Mathematical Physics
Citations in the corpus
- Slope filtrations for relative Frobenius (2006, methodology): “The slope filtration theorem was originally introduced in the context of Berthelot’s rigid cohomology, a p-adic Weil cohomology for varieties in characteristic p. There, one obtains a analogue of the l-adic local monodromy theorem, originally conjectured by Crew [13]; this analogue can be used to es”