Finiteness of rigid cohomology with coefficients

@article{Kedlaya2002FinitenessOR,
  title={Finiteness of rigid cohomology with coefficients},
  author={Kiran S. Kedlaya},
  journal={Duke Mathematical Journal},
  year={2002},
  volume={134},
  pages={15-97}
}
  • K. Kedlaya
  • Published 4 August 2002
  • Mathematics
  • Duke Mathematical Journal
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… 
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Notation 1.1.2. By a k-variety, I meant a reduced (not necessarily irreducible) separated scheme of finite type over k. (It could be shown that the theory only depends on the reduced scheme
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