Relative log convergent cohomology and relative rigid cohomology I

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

2007-07-12

arxiv.org/abs/0707.1742v2

Mathematics

Number Theory

69 pages. Errors and typos fixed

Scientific paper

In this paper, we develop the theory of relative log convergent cohomology. We prove the coherence of relative log convergent cohomology in certain case by using the comparison theorem between relative log convergent cohomlogy and relative log crystalline cohomology, and we relates relative log convergent cohomology to relative rigid cohomology to show the validity of Berthelot's conjecture on the coherence and the overconvergence of relative rigid cohomology for proper smooth families when they admit nice proper log smooth compactification to which the coefficient extends logarithmically.

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