The Grothendieck-Serre Conjecturework of Colliot-Thélène - Ojanguren and Raghunathan

Let A be a regular local ring and G a smooth reductive group scheme over A. Let P be a principal G-bundle over SpecA. Let K be the quotient eld of K. The Grothendieck-Serre conjecture asserts that if the pull-back of P to SpecK is trivial, so is P. In these talks we will prove the conjecture in the following special case: A is the local ring Rp at a closed point p of a smooth scheme over an innite eld k, and G, the pull-back to SpecA of a (smooth reductive) group scheme over k. The result goes back to the early nineties and is due to Colliot-Thélène - Ojanguren (perfect k) and Raghunathan (general k). One of the steps in the proof is the proof in the special case when A is the localisation of k[X]. The proof of this special case involves the Bruhat-Tits theory for groups over local elds and I will start with a brief overview of that theory.

Schedule: There will be three talks of duration 1 hour 30 minutes on 10/11/12 February at 11 a.m.