Mathematical Sciences: The Algebraic Theory of Quadratic Forms and Galois Cohomology

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This project is concerned with the algebraic theory of quadratic forms over fields of characteristic other than two. The principal investigator will study the relationship between the graded Witt ring and galois cohomology rings with coefficients in the integers modulo two. It will be shown that for large classes of fields all these graded rings coincide. To accomplish this, a relative theory of quadratic forms will be developed. This project is concerned with the theory of quadratic forms. A quadratic form is a polynomial function of several variables which is homogeneous of degree two. Quadratic forms over fields of characteristic other than two arise naturally from the symetric inner products on vector spaces over these fields. Thus, the forms are intimately connected to the geometry of the space.