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About: Rigid cohomology     Goto   Sponge   NotDistinct   Permalink

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Type: workyago:WikicatCohomologyTheoriesyago:Abstraction100002137yago:Cognition100023271yago:Explanation105793000yago:HigherCognitiveProcess105770664yago:Process105701363yago:PsychologicalFeature100023100yago:Theory105989479yago:Thinking105770926 New Facet based on Instances of this Class

In mathematics, rigid cohomology is a p-adic cohomology theory introduced by . It extends crystalline cohomology to schemes that need not be proper or smooth, and extends Monsky–Washnitzer cohomology to non-affine varieties. For a scheme X of finite type over a perfect field k, there are rigid cohomology groups Hirig(X/K) which are finite dimensional vector spaces over the field K of fractions of the ring of Witt vectors of k. More generally one can define rigid cohomology with compact supports, or with support on a closed subscheme, or with coefficients in an overconvergent isocrystal. If X is smooth and proper over k the rigid cohomology groups are the same as the crystalline cohomology groups.