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Stable Cohomology of Local Rings and Castelnuovo-Mumford Regularity of Graded Modules
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 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 algebra and to study its commutativity. In Chapter 2 it is proved that if a graded, commutative algebra R over a field k is not Koszul, then the nonzero modules mM, where M is a finitely generated R-module and m is the maximal homogeneous ideal of R, have infinite Castelnuovo-Mumford regularity.
Ferraro, Luigi, "Stable Cohomology of Local Rings and Castelnuovo-Mumford Regularity of Graded Modules" (2017). ETD collection for University of Nebraska-Lincoln. AAI10615063.