Description
Commutative Algebra seminar.
Speaker: R V Gurjar.
Affiliation: IIT Bombay.
Date and Time: Monday 19 August, 3:30 pm - 5:00 pm.
Venue: Room 215, 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. 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