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Shapes of free resolutions over a local ring
We classify the possible shapes of minimal free resolutions over a regular
local ring. This illustrates the existence of free resolutions whose Betti
numbers behave in surprisingly pathological ways. We also give an asymptotic
characterization of the possible shapes of minimal free resolutions over
hypersurface rings. Our key new technique uses asymptotic arguments to study
formal Q-Betti sequences.Comment: 14 pages, 1 figure; v2: sections have been reorganized substantially
and exposition has been streamline
Non-Noetherian Cohen-Macaulay rings
In this paper we investigate a property for commutative rings with identity
which is possessed by every coherent regular ring and is equivalent to
Cohen-Macaulay for Noetherian rings. We study the behavior of this property in
the context of ring extensions (of various types) and rings of invariants.Comment: 16 page
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