Séminaire Algèbre ICJ

Quadratic forms, Brauer groups and twisted moduli spaces

by Raman Parimala

112 (Braconnier)




The existence of nontrivial zeros for quadratic forms of large dimension over the function field of a curve over  a totally imaginary number field is reduced to the bounding of indices of the 2-torsion in the  Brauer group  of the function field. We explain  how  this question  is related to the existence rational points on certain twisted moduli spaces of rank two stable bundles on the curve. Using this method, we explain how  bounds  can be established for the index  in the 2-torsion of the Brauer group for alll genus 2 curves.  (joint work with Jaya N. Iyer)