Description

Mathematics Colloquium Talk 1.

Speaker: R.V. Gurjar.

Affiliation: IIT Bombay.

Date and Time: Wednesday 7 August, 2:45 pm - 3:45 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: 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.

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.

Speaker: R.V. Gurjar.

Affiliation: IIT Bombay.

Date and Time: Wednesday 7 August, 2:45 pm - 3:45 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: 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.

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.

Description

Ramanujan Hall, Department of Mathematics

Date

Wed, August 7, 2019

Start Time

2:45pm-3:45pm IST

Duration

1 hour

Priority

5-Medium

Access

Public

Created by

DEFAULT ADMINISTRATOR

Updated

Mon, August 5, 2019 3:59pm IST