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(TorR(M,N)) is obtained from that of TorG(gr(M),gr(N)) by negative consecutive cancellations, thus extending a theorem of Rossi and Sharifan.
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