This project is concerned with the algebraic theory of quadratic forms over fields of characteristic different from two. The principal investigator will investigate torsion-free properties in the Witt ring using Galois cohomology with coefficients in various Galois modules. He will also study quadratic forms over elliptic curves defined over an arbitrary field. In particular, he will use etale cohomology to investigate the Witt ring of such forms, especially when defined over a local field. 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 symmetric inner products on vector spaces over these fields. Thus the forms are intimately connected to the geometry of the space.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Application #
9001696
Program Officer
Ann K. Boyle
Project Start
Project End
Budget Start
1990-07-01
Budget End
1994-06-30
Support Year
Fiscal Year
1990
Total Cost
$94,700
Indirect Cost
Name
University of California Los Angeles
Department
Type
DUNS #
City
Los Angeles
State
CA
Country
United States
Zip Code
90095