## Crystalline Fundamental Groups II --- Log Convergent Cohomology and Rigid Cohomology

J. Math. Sci. Univ. Tokyo
Vol. 9 (2002), No. 1, Page 1--163.

Shiho, Atsushi
Crystalline Fundamental Groups II --- Log Convergent Cohomology and Rigid Cohomology

Abstract:
In this paper, we investigate the log convergent cohomology in detail. In particular, we prove the log convergent PoincarÃ© 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 coefficient, Berthelot-Ogus theorem for crystalline fundamental groups and independence of compactification for crystalline fundamental groups.

Mathematics Subject Classification (2000): Primary 14F30; Secondary 14F35
Mathematical Reviews Number: MR1889223