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
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Abstract:
In this paper, we investigate the log convergent cohomology in detail. In particular, we prove the log convergent Poincaré 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

Received: 1998-01-14