On the Brauer group of a local field Open Access

Joseph, Adheep (Spring 2022)

Permanent URL: https://etd.library.emory.edu/concern/etds/m613mz79m?locale=en%255D
Published

Abstract

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 Group

Wedderburn's Theorem Central Simple Algebras (Some Results) Skolem-Noether Theorem The Brauer Group Relative Brauer Group

Chapter 2: The Cohomological Brauer Group

Profinite 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 Theory

Cohomological Dimension Brauer Group of a Local Field Some Concluding Remarks

Bibliography

About this Master's Thesis

Rights statement
  • Permission granted by the author to include this thesis or dissertation in this repository. All rights reserved by the author. Please contact the author for information regarding the reproduction and use of this thesis or dissertation.
School
Department
Degree
Submission
Language
  • English
Research Field
Keyword
Committee Chair / Thesis Advisor
Committee Members
Last modified

Primary PDF

Thumbnail Title Date Uploaded Actions
On the Brauer group of a local field () 2022-04-22 14:53:00 -0400

Supplemental Files

Thumbnail Title Date Uploaded Actions