Arithmetic in the Brauer group of the function field of a p-adic curve
Speaker:
Eric Brussel, California State Polytechnic University
Date and Time:
Thursday, June 13, 2013 - 11:00am to 12:00pm
Location:
Fields Institute, Room 230
Abstract:
Joint work with: Kelly McKinnie and Eduardo Tengan. We present machinery that allows us to prove several results concerning the n-torsion subgroup of the Brauer group of the function field F of a p-adic curve, when n is prime to p. We prove that every class of period n is expressible as a sum of two Z/n-cyclic classes, and a more general statement relating symbol lengths of function fields of curves over a complete discretely valued field K and function fields of curves over the residue field of K. We also reprove Saltman's theorem that every division algebra of degree n (not p) over the function field of a p-adic curve is cyclic.