Jason Starr : Rational simple connectedness and Serre's "Conjecture II"

Posted by , part of the Algebraic Geometry Seminar.

At

Jan. 31, 2008, 4 p.m.

In

SEO 636

Abstract

Serre's "Conjecture II" says that every torsor for a simply connected, semisimple algebraic group over a field of "cohomological dimension 2" has a rational point. Using "rational simple connectedness" -- an analogue of simple connectedness where continuous maps from the interval are replaced by morphisms from the projective line -- A. J. de Jong, Xuhua He and I proved this conjecture when group is split and the field is the function field of a surface over an algebraically closed field. Combined with a lot of earlier work by many authors, this settles the conjecture for function fields of surfaces.