On Base Change Theorem and Coherence in Rigid Cohomology
نویسنده
چکیده
We prove that the base change theorem in rigid cohomology holds when the rigid cohomology sheaves both for the given morphism and for its base extension morphism are coherent. Applying this result, we give a condition under which the rigid cohomology of families becomes an overconvergent isocrystal. Finally, we establish generic coherence of rigid cohomology of proper smooth families under the assumption of existence of a smooth lift of the generic fiber. Then the rigid cohomology becomes an overconvergent isocrystal generically. The assumption is satisfied in the case of families of curves. This example relates to P. Berthelot’s conjecture of the overconvergence of rigid cohomology for proper smooth families. 2000 Mathematics Subject Classification: 14F30, 14F20, 14D15
منابع مشابه
Etale Cohomology of Rigid Analytic Spaces
The paper serves as an introduction to etale cohomology of rigid analytic spaces. A number of basic results are proved, e.g. concerning cohomological dimension, base change, invariance for change of base elds, the homotopy axiom and comparison for etale cohomology of algebraic varieties. The methods are those of classical rigid analytic geometry and along the way a number of known results on ri...
متن کاملDigital cohomology groups of certain minimal surfaces
In this study, we compute simplicial cohomology groups with different coefficients of a connected sum of certain minimal simple surfaces by using the universal coefficient theorem for cohomology groups. The method used in this paper is a different way to compute digital cohomology groups of minimal simple surfaces. We also prove some theorems related to degree properties of a map on digital sph...
متن کاملGlobally analytic $p$-adic representations of the pro--$p$--Iwahori subgroup of $GL(2)$ and base change, I : Iwasawa algebras and a base change map
This paper extends to the pro-$p$ Iwahori subgroup of $GL(2)$ over an unramified finite extension of $mathbb{Q}_p$ the presentation of the Iwasawa algebra obtained earlier by the author for the congruence subgroup of level one of $SL(2, mathbb{Z}_p)$. It then describes a natural base change map between the Iwasawa algebras or more correctly, as it turns out, between the global distribut...
متن کاملEnhanced Six Operations and Base Change Theorem for Artin Stacks
In this article, we develop a theory of Grothendieck’s six operations for derived categories in étale cohomology of Artin stacks. We prove several desired properties of the operations, including the base change theorem in derived categories. This extends all previous theories on this subject, including the recent one developed by Laszlo and Olsson, in which the operations are subject to more as...
متن کاملEquivariant Crystalline Cohomology and Base Change
Given a perfect field k of characteristic p > 0, a smooth proper k-scheme Y , a crystal E on Y relative to W (k) and a finite group G acting on Y and E, we show that, viewed as a virtual k[G]-module, the reduction modulo p of the crystalline cohomology of E is the de Rham cohomology of E modulo p. On the way we prove a base change theorem for the virtual Grepresentations associated with G-equiv...
متن کامل