Harvey, Ebony Ann. “Cohomological Invariants of Quadratic Forms”, Boston College, 2010. http://hdl.handle.net/2345/1324.
Given a field F, an algebraic closure K and an F-vector space V, we can tensor the space V with the algebraic closure K. Two quadratic spaces of the same dimension become isomorphic when tensored with an algebraic closure. The failure of this isomorphism over F is measured by the Hasse invariant. This paper explains how the determinants and Hasse Invariants of quadratic forms are related to certain cohomology classes constructed from specific short exact sequences. In particular, the Hasse Invariant is defined as an element of the Brauer group.