A Hasse principle for homogeneous spaces over function fields of p-adic curves

Series: 
School of Mathematics Colloquium
Thursday, February 18, 2010 - 16:00
1 hour (actually 50 minutes)
Location: 
Skiles 269
,  
Department of Mathematics and Computer Science, Emory University
Let k be a p-adic field and K/k function field in one variable over k. We discuss Hasse principle for existence of rational points on homogeneous spaces under connected linear algebraic groups. We illustrate how a positive answer to Hasse principle leads for instance to the result: every quadratic form in nine variables over K has a nontrivial zero.