Algebraic Geometry Seminar
Jason Starr
SUNY Stony Brook
Rational simple connectedness and Serre's "Conjecture II"
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.
Thursday January 31, 2008 at 4:00 PM in SEO 636