Consecutive cancellations in Tor modules over local rings

Abstract

Let $M,N$ be finite modules over a Noetherian local ring $R$, and let $G$ be the associated graded ring of $R$. We show that the bigraded Hilbert series of $gr(To{r}^R(M,N))$ is obtained from that of $To{r}^G(gr(M),gr(N))$ by negative consecutive cancellations, thus extending a theorem of Rossi and Sharifan.

7 pages

References in corpus (1)

• Consecutive cancellations in Betti numbers of local rings

Cited by in corpus (2)

• On the parity conjecture for Hilbert schemes of points on threefolds
• On the multiplicity of tangent cones of monomial curves