SR 511

If q is a quadratic form over a field k, then its splitting pattern is defined as the set of Witt indices realised by q over all field extensions of k. It is an important open problem to determine all possible splitting patterns of quadratic forms over a general field. Over fields of characteristic different from 2, substantial progress has been made on this problem through the study of algebraic cycles on certain algebraic varieties naturally associated to quadratic forms. At present, some of the general algebro-geometric machinery which has been central to these developments is unavailable over fields of characteristic 2. As a result, much less is known about the splitting of quadratic forms in this setting. In this talk I will discuss some new results in this direction for Fermat-type quadratic forms over fields of characteristic 2 (so-called quasilinear quadratic forms) which can be proved using purely algebraic methods.

Stephen Scully

University of Nottingham