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Summary: COMPLETE INTERSECTION DIMENSION
Luchezar L. Avramov, Vesselin N. Gasharov, and Irena V. Peeva
Abstract. A new homological invariant is introduced for a nite module over a commutative
noetherian ring: its CI-dimension. In the local case, sharp quantitative and structural data are
obtained for modules of nite CI-dimension, providing the rst class of modules of (possibly)
in nite projective dimension with a rich structure theory of free resolutions.
Contents
Introduction
1. Homological dimensions
2. Quantum regular sequences
3. Constructions of modules of nite CI-dimension
4. Cohomology operators
5. Complexity
6. Homological reductions
7. Critical degree and growth of Betti numbers
8. Asymptotes of Betti sequences
9. Obstructions to embeddings into standard resolutions
References
Introduction
Let M be a nite module over a commutative noetherian local ring R. There always
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