Mathematical Sciences: Quadratic Forms, Division Algebras and Galois Cohomology

点击翻译按钮获取中文摘要

This project studies several problems in the algebraic theory of quadratic forms and the structure of finite-dimensional division algebras over arbitrary fields. These problems are studied using the tools of Galois theory and Galois cohomology. This research concerns the theory of quadratic forms which is a study of the solutions of homogeneous second degree polynomials, or equivalently, the study of the geometry of spaces possessing a symmetric inner product. The project outlined concerns some of the most important problems in the area of quadratic forms.