MATH Seminar

Title: Local-global principles for torsors over arithmetic curves
Seminar: Algebra and Number Theory
Speaker: David Harbater of University of Pennsylvania
Contact: R. Parimala, parimala@mathcs.emory.edu
Date: 2012-04-13 at 3:00PM
Venue: W304
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Abstract: This talk, on joint work with Julia Hartmann and Daniel Krashen, concerns local-global principles over function fields of curves that are defined over a complete discretely valued field. Classically, one studies such principles over number fields, or over function fields of curves defined over a finite field. In that situation, if $G$ is an algebraic group, one can ask whether a $G$-torsor (principal homogeneous space for $G$) over the field must be trivial whenever it is locally trivial. This does not always hold, but the obstruction is always finite if $G$ is a linear algebraic group. This talk will study the analogous question in our situation. Applications include results about quadratic forms and central simple algebras.