This award supports investigations into the algebraic theory of quadratic forms over fields of characteristic different from two and over schemes proper over such fields, especially complete regular curves with a rational point. In particular, the principal investigator will investigate symmetric bilinear spaces over a scheme and their equivalence classes in the Witt ring utilizing geometric and etale methods. He will also study Galois cohomology with 2-adic coefficients and its relationship to quadratic form theoretic questions. The research supported involves the theory of quadratic forms. This, in its simplest form, is the study of polynomial forms of degree two. Equivalently, it is an analysis of the types of inner products that can define the metric geometry of an n-dimensional vector space. The study of quadratic forms has deep interrelations with algebraic geometry and algebraic k-theory.
