This thesis focuses on the study of Brauer groups via Galois Cohomology. In particular, it will cover Wedderburn theory of central simple algebras over general fields, group cohomology and Galois Cohomology, generic splitting, and a description of the Brauer group as a Galois Cohomology group. With a blend of arithmetic results from class field theory, the main aim of the thesis will be the determination of the Brauer group of a local field and establishing the reciprocity sequence for the Brauer group of a number field.
Table of Contents
Chapter 1: Central Simple Algebras and The Brauer GroupWedderburn's Theorem Central Simple Algebras (Some Results) Skolem-Noether Theorem The Brauer Group Relative Brauer Group
Chapter 2: The Cohomological Brauer GroupProfinite Groups Cohomology of Profinite Groups Hilbert's Theorem 90 Brauer Group as Galois Cohomology Group Some Computations Central Simple Algebras Over Complete Discrete Valued Fields
Chapter 3: Applications to Class Field TheoryCohomological Dimension Brauer Group of a Local Field Some Concluding Remarks
About this Master's Thesis
|Committee Chair / Thesis Advisor|
|On the Brauer group of a local field ()||2022-04-22 14:53:00 -0400||