Publication Date

2003

Document Type

Dissertation/Thesis

First Advisor

Seelinger, George Francis, 1963-||Blair, William D.

Degree Name

Ph.D. (Doctor of Philosophy)

Department

Department of Mathematical Sciences

LCSH

Cocycles||Geometry, Algebraic||Algebra, Homological

Abstract

The theory of weak 2-cocycles is a generalization of the classical theory of Galois 2-cocycles, in that the weak 2-cocycles can take on zero values in a field instead of the abelian group of units in the field. For a fixed base field and a fixed Galois group, the corresponding weak 2-cocycles then form an affine variety. We show that this variety is a singular toric variety. Then we use the toric variety structure to discuss the Cohen-Macaulayness of the variety and the freeness of finitely generated projective modules over the coordinate ring of that variety. We also consider idempotent weak 2-cocyles and show that these idempotents stratify the variety of weak 2-cocycles. This stratification allows us to further analyze the geometry of the variety.

Comments

Includes bibliographical references (pages [58]-59).

Extent

59 pages

Language

eng

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

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