Relative log convergent cohomology and relative rigid cohomology II

Details Relative log convergent cohomology and relative rigid cohomology II Relative log convergent cohomology and relative rigid cohomology II

2007-07-12

arxiv.org/abs/0707.1743v2

Mathematics

Number Theory

80 pages, minor errors and typos fixed

Scientific paper

In this paper, we develop the theory of relative log convergent cohomology of radius $\lambda$ ($0 < \lambda \leq 1$), which is a generalization of the notion of relative log convergent cohomology in the previous paper. By comparing this cohomology with relative log crystalline cohomology, relative rigid cohomology and its variants and by using some technique of hypercovering, we prove a version of Berthelot's conjecture on the overconvergence of relative rigid cohomology for proper smooth families.

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