Vortrag im Schwerpunkt Reelle Geometrie und Algebra
Donnerstag, 27. August 2009, um 17:00 Uhr in F426 (Schwerpunktkolloquium) Moshe Jarden (Tel-Aviv) Function Fields of One Variable over PAC Fields
Let K be a PAC field containing all roots of unity. We prove Serre's Conjecture II for function fields F of one variable over
K when char(K) = 0, namely H^1(Gal(F),G) = 1 for each simply connected semi-simple linear algebraic group G.
We also prove for an arbitrary PAC field K and a variable x that Gal(K(x)_ab) is a free profinite group of rank card(K). This
is a stronger version of a conjecture of Bogomolov for K(x) and an analog of a conjecture of Shafarevich that Gal(Q_ab) is isomorphic to F^_&Omega.
Both results appear in a joint work with Florian Pop.
