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Stable Cohomology Of Local Rings And Castelnuovo-Mumford Regularity Of Graded Modules, Luigi Ferraro
Stable Cohomology Of Local Rings And Castelnuovo-Mumford Regularity Of Graded Modules, Luigi Ferraro
Department of Mathematics: Dissertations, Theses, and Student Research
This thesis consists of two parts:
1) A bimodule structure on the bounded cohomology of a local ring (Chapter 1),
2) Modules of infinite regularity over graded commutative rings (Chapter 2).
Chapter 1 deals with the structure of stable cohomology and bounded cohomology. Stable cohomology is a $\mathbb{Z}$-graded algebra generalizing Tate cohomology and first defined by Pierre Vogel. It is connected to absolute cohomology and bounded cohomology. We investigate the structure of the bounded cohomology as a graded bimodule. We use the information on the bimodule structure of bounded cohomology to study the stable cohomology algebra as a trivial extension …