Symmetries in Bass and Betti sequences over a complete intersection ring

Abstract: Despite homological algebra over a complete intersection ring being unbounded, resolutions enjoy polynomial growth. That is to say, for a finitely generated module over a complete intersection ring, its sequence of Bass numbers and its sequence Betti numbers are eventually given by quasi-polynomials with period two; the leading terms of the quasi-polynomials are independent of the parity. In this talk, I will discuss joint worth with Briggs and McCormick where we show the leading terms of the two quasi-polynomials agree. The main tool is a higher order support theory which generalizes the well-studied support varieties of a complete intersection ring.

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

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