Soumi Tikader :ISI Kolkata

Description
Commutative Algebra seminar I.

Speaker: Soumi Tikader.

Affiliation: ISI Kolkata.

Date and Time: Monday 21 October, 11:30 am - 12:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Orbit spaces of unimodular rows over smooth real affine algebras.

Abstract: In this talk we will discuss about the group structure on orbit
spaces of unimodular rows over smooth real affine algebras. With a few
definition and some results to start, we will prove a structure theorem of
elementary orbit spaces of unimodular rows over aforementioned ring with
the help of similar kind results on Euler class group. As a consequences,
we will prove that :

Let $X=Spec(R)$ be a smooth real affine variety of even dimension $d > 1$,
whose real points $X(R)$ constitute an orientable manifold. Then the set
of isomorphism classes of (oriented) stably free $R$ of rank $d > 1$ is a
free abelian group of rank equal to the number of compact connected
components of $X(R)$.

In contrast, if $d > 2$ is odd, then the set of isomorphism classes of
stably free $R$-modules of rank $d$ is a $Z/2Z$-vector space (possibly
trivial). We will end this talk by giving a structure theorem of Mennicke
symbols.
Description
Ramanujan Hall, Department of Mathematics
Date
Mon, October 21, 2019
Start Time
11:30am-12:30pm IST
Duration
1 hour
Priority
5-Medium
Access
Public
Created by
DEFAULT ADMINISTRATOR
Updated
Mon, October 21, 2019 11:39am IST