Crystalline Fundamental Groups II — Log Convergent Cohomology and Rigid Cohomology

In this paper, we investigate the log convergent coho- mology in detail. In particular, we prove the log convergent Poincare lemma and the comparison theorem between log convergent cohomology and rigid cohomology in the case that the coefficient is an F a -isocrystal. We also give applications to finiteness of rigid cohomology with coeffi- cient, Berthelot-Ogus theorem for crystalline fundamental groups and independence of compactification for crystalline fundamental groups.

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