Loop torsors in arithmetic geometry

The four lectures are based on recent and running joint work with Chernousov and Pianzola. Given an algebraic group G and an algebraic variety X, loop G-torsors are those arising from change of groups from the algebraic fundamental groups of X. After a few generalities, we should discuss the case of split tori and the classi cation of loop torsors in this case. Next we shall see that the de nitions extend well in the so-called Abyankar setting, that is, over a localization of a henselian regular local ring with respect to a normal crossing divisor. In this case, there is a weak classi cation of loop torsors (involving Galois cohomology and Bruhat-Tits theory). It applies to the study of local-global principles for non-abelian Galois of semiglobal elds (joint work with Parimala).

Schedule:March 3, 5, 10, 12 at 2:30 p.m.