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.

Dear all,
 Prof. Nitin Nitsure will give a series of lectures on 'Algebraic Stacks
and Moduli Theory' starting next week. The draft announcement is
attached.
The first talk will be introductory and will be accessible to everyone
with very minimal knowledge of algebraic geometry.

For the benefit of students, this is a very central and important area of
algebraic geometry and Prof. Nitsure is a very good lecturer. Do try and
attend the first lecture in Ramanujan Hall on Tuesday 27th at 5:10 pm. The
first talk will be of 1 hour.