Cohomologie log plate, actions modérées et structures galoisiennes

Details Cohomologie log plate, actions modérées et structures galoisiennes Cohomologie log plate, actions modérées et structures galoisiennes

2009-05-12

arxiv.org/abs/0905.1902v3

Mathematics

Algebraic Geometry

35 pages, LaTeX. Proof of Lemme 3.3 corrected. Minor modifications. Accepted for publication in Crelle's Journal

Scientific paper

Let $X$ be a fine and saturated log scheme, and let $G$ be a commutative finite flat group scheme over the underlying scheme of $X$. If $G$-torsors for the fppf topology can be thought of as being unramified objects by nature, then $G$-torsors for the log flat topology allow us to consider tame ramification. Using the results of Kato, we define a concept of Galois structure for these torsors, then we generalize the author's previous constructions (class-invariant homomorphism for semi-stable abelian varieties) in this new setting, thus dropping some restrictions.

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