Crystalline fundamental groups. II: Log convergent cohomology and rigid cohomology. (English) Zbl 1057.14025

Shiho, Atsushi

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

From the text: This is a continuation of a previous paper of the author [J. Math. Sci. Univ. Tokyo 7, 509–656 (2000; Zbl 0984.14009)]. There, we gave a definition of crystalline fundamental groups for certain fine log schemes over a perfect field of positive characteristic and proved some fundamental properties of them.
Here, 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 [A. Shiho, loc. cit.] and independence of compactification for crystalline fundamental groups.

MSC:

14F30	\(p\)-adic cohomology, crystalline cohomology
14F35	Homotopy theory and fundamental groups in algebraic geometry
14G22	Rigid analytic geometry
14G20	Local ground fields in algebraic geometry
14F43	Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)

Keywords:

rigid analytic geometry; isocrystals

Citations:

Zbl 0984.14009