Wednesday 22 March 2017, 16:00-17:00 in HG03.085
Marta Pieropan (FU Berlin)
On rationally connected varieties over large C_1 fields of characteristic 0
In the 1950s Lang studied the properties of C_1 fields, that is, fields over which every hypersurface of degree at most n in an n-dimensional projective space has a rational point. Later he conjectured that every smooth proper rationally connected variety over a C_1 field has a rational point. The conjecture is proven for finite fields (Esnault) and function fields of curves over algebraically closed fields (Graber-Harris-de Jong-Starr). I use birational geometry to address the open case of Henselian fields of mixed characteristic with algebraically closed residue field.