Description

Commutative Algebra seminar.

Speaker: R V Gurjar.

Affiliation: IIT Bombay.

Date and Time: Monday 26 August, 3:30 pm - 5:00 pm.

Venue: Room 215, Department of Mathematics.

Title: Lecture series on Ramification in Commutative Algebra and Algebraic

Geometry.

Abstract: We will consider mainly the following situation. Let R,S be

complete normal local domains over an alg. closed field k of char. 0 such

that S is integral over R. Our aim is to describe three ideals in S; I_N,

I_D, I_K (Noether, Dedekind, Kahler differents resp.) each of which

capture the ramified prime ideals in S over R. In general these three

ideals are not equal. An important special case when all are equal is when

S is flat over R. We will prove many of these statements.

The case when there is a finite group G of k-automorphisms of S such that

R is the ring of invariants is already very interesting. Then many nice

results are proved.

These include works of Auslander-Buchsbaum, Chevalley-Shephard-Todd,

Balwant Singh, L. Avramov, P. Roberts, P. Griffith, P. Samuel....

I will try to discuss all these results.

I believe that these results and ideas involved in them will be very

valuable to students and faculty both.

Prerequisites. Basic knowledge of Commutative Algebra and language of

Algebraic Geometry (no sheaf theory!). I will "throw in" topological

proofs from time to time to make the results intuitively more clear.

Speaker: R V Gurjar.

Affiliation: IIT Bombay.

Date and Time: Monday 26 August, 3:30 pm - 5:00 pm.

Venue: Room 215, Department of Mathematics.

Title: Lecture series on Ramification in Commutative Algebra and Algebraic

Geometry.

Abstract: We will consider mainly the following situation. Let R,S be

complete normal local domains over an alg. closed field k of char. 0 such

that S is integral over R. Our aim is to describe three ideals in S; I_N,

I_D, I_K (Noether, Dedekind, Kahler differents resp.) each of which

capture the ramified prime ideals in S over R. In general these three

ideals are not equal. An important special case when all are equal is when

S is flat over R. We will prove many of these statements.

The case when there is a finite group G of k-automorphisms of S such that

R is the ring of invariants is already very interesting. Then many nice

results are proved.

These include works of Auslander-Buchsbaum, Chevalley-Shephard-Todd,

Balwant Singh, L. Avramov, P. Roberts, P. Griffith, P. Samuel....

I will try to discuss all these results.

I believe that these results and ideas involved in them will be very

valuable to students and faculty both.

Prerequisites. Basic knowledge of Commutative Algebra and language of

Algebraic Geometry (no sheaf theory!). I will "throw in" topological

proofs from time to time to make the results intuitively more clear.

Description

Room No. 215 Department of Mathematics

Date

Mon, August 26, 2019

Start Time

3:30pm-5:00pm IST

Duration

1 hour 30 minutes

Priority

5-Medium

Access

Public

Created by

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Updated

Mon, August 26, 2019 10:33am IST