#### Ramanujan Auditorium

#### Quadratic forms over function fields

#### R. Parimala

##### Emory University

*Quadratic forms over number fields are well understood via class field theory. Every quadratic form in at least five variables over a totally imaginary number field admits a nontrivial zero. It is an open question whether quadratic forms in large enough*

number of variables over function fields of curves over totally imaginary number fields admit a nontrivial zero. The expectation is that every quadratic form in at least nine variables over such a field represents zero nontrivially. Over function fields of

p-adic curves, every quadratic form in nine variables admits a nontrivial zero. We shall explain a method of attack of the problem via Galois cohomology invariants.

Done