ALMOST ETALE EXTENSIONS OF FONTAINE RINGS AND LOG-CRYSTALLINE COHOMOLOGY IN THE SEMI-STABLE REDUCTION CASE

作者：Lodh Remi Shankar^*

来源：Annales de l'Institut Fourier, 2011, 61(5): 1875-1942.

• p-adic Hodge theory
• almost etale extensions
• crystalline cohomology
• log-structures

Let K be a field of characteristic zero complete for a discrete valuation, with perfect residue field of characteristic p > 0, and let K+ be the valuation ring of K. We relate the log-crystalline cohomology of the special fibre of certain affine K+-schemes X = Spec(R) with good or semi-stable reduction to the Galois cohomology of the fundamental group pi(1) (X-(K) over bar) of the geometric generic fibre with coefficients in a Fontaine ring constructed from R. This is based on Faltings' theory of almost etale extensions.

• 出版日期2011