Homogeneous spaces over function fields of p-adic curves

Mardi 9 juin 2009 16:00-17:00 - Parimala Raman - Emory University (Atlanta)

Résumé : Let K be a p-adic field and F = K(X) the function field of a curve over K. We discuss the following local-global principle : given a principal homogeneous space Y under a connected linear algebraic group G defined over F , whether the existence of rational points in each completion of F with respect to discrete valuations of F implies the existence of F -rational points on Y . An essential use is made of recent patching results of Harbater-Hartman-Krashen. We draw a connection to the injectivity of the Rost invariant.
(Joint work with J.-L. Colliot-Thélène and V.Suresh)

Lieu : bât. 425 - 113-115

Homogeneous spaces over function fields of p-adic curves  Version PDF