SR 511

We consider generalizations of a celebrated theorem of Merkurjev--every 2-torsion Brauer class is represented by the Clifford algebra of a quadratic form--to base schemes other than fields. Parimala, Scharlau, and Sridharan showed that over smooth complete p-adic hyperelliptic curves, the validity of Merkurjev`s theorem is equivalent to the existence of a rational theta characteristic. The main result we`ll discuss is that over smooth complete p-adic curves or surfaces over finite fields, considering the Clifford invariants of quadratic forms with values in line bundles yields a generalized form of Merkurjev`s theory in complete generality.

Asher Auel

MPIM Bonn und Emory University, Atlanta, USA