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

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)
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