Seelinger, George Francis, 1963-||Blair, William D.
Ph.D. (Doctor of Philosophy)
Department of Mathematical Sciences
Cocycles||Geometry, Algebraic||Algebra, Homological
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.
Shahverdian, Jill, "The geometry of weak 2-cocycles" (2003). Graduate Research Theses & Dissertations. 5803.
Northern Illinois University
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