Quasi-polynomial growth of Betti sequences - with Luchezar Avramov and Nicholas Packauskas

Abstract: Let Q be a regular local ring and I an ideal generated by a regular sequence of c elements in the square of the maximal ideal. It is known that over the complete intersection R = Q/I that any finitely generated module M has Betti numbers eventually given by quasi-polynomial of degree less than c. That is, there are integer-valued polynomial functions p M + and p M − with the same leading term such that β R 2i (M) = p M + (2i) and β R 2i+1(M) = p M − (2i + 1) for i sufficiently large. We will show that if q is the height of the ideal generated by the quadratic initial forms of I in the associated graded ring of Q, then the degree of p M + − p M − is less than c − q − 1.

commutative algebraalgebraic topologyquantum algebrarepresentation theory

Audience: researchers in the topic

DG methods in commutative algebra and representation theory

Series comments: Description: Online special session

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