On base change theorem and coherence in rigid cohomology
type: Item
instance of: scholarly article
title: On base change theorem and coherence in rigid cohomology
zbMATH Open document ID: 1093.14503
author: Nobuo Tsuzuki
published in: Documenta Mathematica
publication date: 2004-01-19T00:00:00Z
full work available at URL: https://eudml.org/doc/126280
full work available at URL: tsuzuki.dm.html
review text: Summary: 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.
Mathematics Subject Classification ID: 14F30
Mathematics Subject Classification ID: 14F20
Mathematics Subject Classification ID: 14D15
zbMATH DE Number: 2028853
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2028853