Beginning in 2006, the UChicago Chapter of the AWM has hosted a series colloquia by distinguished women in math.
- Wednesday, October 14, 2015, 4:30PM, Eckhart 133
- R. Parimala (Emory University)
- Quadratic forms over function fields of p-adic curves
Quadratic forms over the field of real numbers are determined by their dimension and signature. Over p-adic fields, they are classified by dimension, discriminant and Clifford invariant. Every 5-dimensional quadratic form over a p-adic field has a nontrivial zero. Hasse-Minkowski theorem asserts that a quadratic form over a number field has a nontrivial zero provided it has a nontrivial zero over its completions at all places. In particular every 5-dimensional indefinite quadratic form over a number field has a nontrivial zero. Similar questions on local-global principles for nontrivial zeros of quadratic forms over function fields of curves over totally imaginary number fields and p-adic fields have been posed; positive answers to these questions have deep consequences for the study of quadratic forms over these fields. We discuss some recent progress in this direction for function fields of p-adic curves.