Shapes of free resolutions over a local ring

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

Research output: Contribution to journalArticle

5 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 languageEnglish (US)
Pages (from-to)939-954
Number of pages16
JournalMathematische Annalen
Volume354
Issue number3
DOIs
StatePublished - 2012

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