Heilbronn Number Theory: On rationally connected varieties over large C_1 fields of characteristic 0
Title: On rationally connected varieties over large C_1 fields of characteristic 0
Abstract: In the 1950s Lang studied the properties of C_1 fields, that is, fields over which every homogeneous polynomial of degree at most n in n+1 variables has a nontrivial solution. 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). This talk addresses the open case of Henselian fields of mixed characteristic with algebraically closed residue field.