Cohomologie syntomique: liens avec les cohomologies étale et rigide

Details Cohomologie syntomique: liens avec les cohomologies étale et rigide Cohomologie syntomique: liens avec les cohomologies étale et rigide

2009-10-23

arxiv.org/abs/0910.4436v1

Mathematics

Algebraic Geometry

26 pages

Scientific paper

Syntomic cohomology here defined yields a link between rigid cohomology and etale cohomology, viewing the last one as the fixed points under Frobenius of the former one. Let V be a complete discrete valuation ring, with perfect residue field k = V/m of characteristic p > 0 and fraction field K of characteristic 0. Having defined syntomic cohomology with compact supports of an abelian sheaf G on a k-scheme X, we show that it coincides with etale cohomology with compact supports when G is a lisse sheaf. If moreover the convergent F-isocrystal associated to G comes from an overconvergent isocrystal E, then the rigid cohomology of E expresses as a limit of syntomic cohomologies: then the etale cohomology with compact supports of G is the fixed points of Frobenius acting on the rigid cohomology of E.

Affiliated with

Also associated with

No associations

Rating

Cohomologie syntomique: liens avec les cohomologies étale et rigide does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Cohomologie syntomique: liens avec les cohomologies étale et rigide, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cohomologie syntomique: liens avec les cohomologies étale et rigide will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-423264