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- Title
Shapes of free resolutions over a local ring.
- Authors
Berkesch, Christine; Erman, Daniel; Kummini, Manoj; Sam, Steven
- 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 $${\mathbb {Q}}$$ -Betti sequences.
- Subjects
BETTI numbers; HOMOLOGY theory; HYPERSURFACES; MATHEMATICAL sequences; MATHEMATICAL analysis
- Publication
Mathematische Annalen, 2012, Vol 354, Issue 3, p939
- ISSN
0025-5831
- Publication type
Article
- DOI
10.1007/s00208-011-0760-2