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Polynomial Growth Of Betti Sequences Over Local Rings, Luchezar L. Avramov, Alexandra Seceleanu, Zheng Yang
Polynomial Growth Of Betti Sequences Over Local Rings, Luchezar L. Avramov, Alexandra Seceleanu, Zheng Yang
Department of Mathematics: Faculty Publications
We study sequences of Betti numbers (βRi (M)) of finite modules M over a complete intersection local ring, R. It is known that for every M the subsequence with even, respectively, odd indices i is eventually given by some polynomial in i. We prove that these polynomials agree for all R-modules if the ideal I☐ generated by the quadratic relations of the associated graded ring of R satisfies height I☐ ≥ codim R − 1, and that the converse holds when R is homogeneous and when codim R ≤ 4. Avramov, …