Year of Award

2018

Document Type

Dissertation - Campus Access Only

Degree Type

Doctor of Philosophy (PhD)

Degree Name

Mathematics

Department or School/College

Department of Mathematical Sciences

Committee Chair

Kelly McKinnie

Commitee Members

Eric Chesebro, Nikolaus Vonessen, Elizabeth Gillaspy, Oliver Serang

Keywords

Brauer Group, Central Simple Algebras, Cyclic algebras, Essential Dimension, Kummer Subspaces, Non Commutative Algebra

Publisher

University of Montana

Abstract

We separate this dissertation into three distinct but related parts. Chapter one focuses on p-Kummer subspaces of G-crossed products where G is an elementary abelian group. We show that if A is a generic G-crossed product with not strong degenerate u matrix, all p-Kummer subspaces are of dimension 1 over the center. The second chapter makes use of the essential dimension of (Z=pZ)r over a eld of characteristic p. We provide an upper bound of the essential dimension of the functor Decn+1;p` as well as a concrete construction of the eld and algebra of descent for the functor Dec2;pr . Chapter three explores the Galois symbol and related objects. We make use of divided power maps on the the cohomology groups Hn(K; n p ) to provide a lower bound for the functor hn; 'p.

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© Copyright 2018 Nhan Trong Nguyen