Crystalline Fundamental Groups I --- Isocrystals on Log Crystalline Site and Log Convergent Site

J. Math. Sci. Univ. Tokyo
Vol. 7 (2000), No. 4, Page 509--656.

Shiho, Atsushi
Crystalline Fundamental Groups I --- Isocrystals on Log Crystalline Site and Log Convergent Site
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Abstract:
In this paper, we define the crystalline fundamental groups for fine log schemes (satisfying certain condition) over a perfect field of positive characteristic by using the category of isocrystals on log crystalline site and prove their fundamental properties, such as Hurewicz isomorphism, the bijectivity of crystalline Frobenius and the comparison theorem with (log version of) de Rham fundamental groups (log version of Berthelot-Ogus theorem for fundamental groups).

Mathematics Subject Classification (1991): Primary 14F30; Secondary 14F35, 14F40, 18E10
Mathematical Reviews Number: MR1800845

Received: 1997-07-15