Cohomologie log plate, actions mod\'er\'ees et structures galoisiennes

TL;DR

This paper extends the theory of torsors in logarithmic geometry to include tame ramification by defining Galois structures for log flat torsors, generalizing previous class-invariant homomorphisms.

Contribution

It introduces a Galois structure concept for log flat torsors, broadening the scope of ramification considerations in logarithmic schemes.

Findings

Defines Galois structures for log flat torsors using Kato's results

Generalizes class-invariant homomorphisms to new settings

Drops previous restrictions in the theory

Abstract

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.