Algebraic Geometry Seminar

Date

Tuesday, 12 March, 11.30 am

Venue

Room 215

Host

Sudarshan Gurjar

speaker

Nitin Nitsure

Affiliation

Bhaskaracharya Pratishthana

Title

Galois descent, twisted forms, and Galois cohomology.

Abstract

We will first briefly recall faithfully flat descent (which was done in detail in the previous talk), and the geometry of finite Galois covers and their fiber powers (which was done in detail earlier). Then we will translate faithfully flat descent into Galois covering terms, to arrive at a formulation of descent and effective descent purely in terms of Galois groups and their actions. We will then show how to parameterize twisted forms of various structures via the first Galois cohomology. We will illustrate everything with examples from algebra and algebraic geometry. Finally, we will address the question of effective Galois descent for schemes.

Algebraic groups seminar

Date

 Tuesday, 12 March, 4 pm

Venue

Ramanujan Hall

Host

Shripad Garge

speaker

Akash Yadav

Affiliation

IIT Bombay

Title

Complete varieties I

Abstract

We introduce the notion of complete varieties to study parabolic subgroups of linear algebraic groups. 

Commutative Algebra Seminar

Date

Tuesday, 12 Mar, 4 pm—5 pm

Venue

Room 215

Host

Tony J. Puthenpurakal

speaker

Omkar Javadekar 

Affiliation

IIT Bombay

Title

A theorem of Bruns on free resolutions of ideals generated by three elements-II

Abstract

Let R be a commutative Noetherian ring. In 1972, P. Cohn proved that for every finitely generated R-module M, there exists a three-generated ideal I of R such that pdim(M)=pdim(R/I). In this series of two talks, we will see a generalization of Cohn's result due to W. Bruns. We will show that "every" finite free resolution over R is a free resolution of a three-generated ideal of R.