Log flat cohomology, tame actions, and Galois structures (Q2890359)

The paper deals with extensions of torsors. Assume \(G\) is a finite flat group scheme over a scheme \(X,U\subset X\) an open subset, and we are given a \(G\)-torsor over \(U\). One way to control its bad reduction along \(D= X- U\) is to use logarithmic geometry and to assume that our tensor extends to a torsor in some logarithmic sense. Here the author uses the ``Kummer flat topology''. For technical reasons he usually assumes that \(X\) is regular and \(D\) a divisor with normal crossings.NEWLINENEWLINE The main results are existence of invariants for points on Neron models of abelian varieties, extending known results from good to semistable reduction.