Description

Commutative algebra seminar Tuesday, 27 September 2022 @3.30 pm. Venue: Ramanujan Hall Speaker: Tony Puthenpurakal, IIT Bombay Title: On coefficient ideals-II Abstract: Let (A, m) be a Cohen-Macaulay local ring of dimension d ≥ 2 with infinite residue field and let I be an m-primary ideal. Let For 0 ≤ i ≤ d let Ii be the i th-coefficient ideal of I. Also let Ie = Id denote the Ratliff-Rush closure of A. Let G = GI (A) be the associated graded ring of I. We show that if dim H j G+ (G) ∨ ≤ j−1 for 1 ≤ j ≤ i ≤ d−1 then (I n)d−i = Ifn for all n ≥ 1. In particular if G is generalized Cohen-Macaulay then (I n)1 = Ifn for all n ≥ 1. As a consequence we get that if A is an analytically unramified domain with G generalized Cohen-Macaulay, then the S2-ification of the Rees algebra A[It] is L n≥0 Ifn.

Description

Ramanujan Hall, Department of Mathematics

Date

Tue, September 27, 2022

Start Time

3:30pm IST

Priority

5-Medium

Access

Public

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Updated

Mon, September 26, 2022 10:29am IST