Shapes of free resolutions over a local ring

Christine Berkesch; Daniel Erman; Manoj Kummini; Steven V. Sam

doi:10.1007/s00208-011-0760-2

Shapes of free resolutions over a local ring

Christine Berkesch, Daniel Erman, Manoj Kummini, Steven V. Sam

School of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	939-954
Number of pages	16
Journal	Mathematische Annalen
Volume	354
Issue number	3
DOIs	https://doi.org/10.1007/s00208-011-0760-2
State	Published - Nov 2012

Bibliographical note

Funding Information:
CB was supported by NSF Grant OISE 0964985, DE by an NDSEG fellowship and NSF Award No. 1003997, and SVS by an NSF graduate research fellowship and an NDSEG fellowship.

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AU - Sam, Steven V.

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N2 - 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.

AB - 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.

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Shapes of free resolutions over a local ring

Abstract

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