2.45 p.m. On the extension of torsors Marco Antei Ben Gurion University of the Negev, Be'er Sheva, Israel. 110713 Abstract Let S be the spectrum of a discrete valuation ring and $\eta=Spec(K)$ its generic point; let X be a scheme, faithfully flat and of finite type over S (e.g. a fibered surface) and $f_{\eta}: X_{\eta}\to \eta$ its generic fibre (e.g. a curve, if X is a fibered surface). Assume we are given a finite Kgroup scheme G and a Gtorsor $Y\to X_{\eta}$ (the definition will be recalled). So far the problem of extending the Gtorsor $Y\to X_{\eta}$ has consisted in finding a finite and flat Sgroup scheme G' whose generic fibre is isomorphic to G and a G'torsor $T\to X$ whose generic fibre is isomorphic to $Y\to X_{\eta}$ as a Gtorsor. Some solutions to this problem are known in some particular relevant cases and will be recalled, from the first attempt due to Grothendieck to the most recent results. At the end of the talk we will suggest a new point of view.
