Description

Monday, 11 December, 11:30 am

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Host: Sudarshan Gurjar

Venue: Ramanujan Hall

Speaker: Nitin Nitsure,

Affiliation: TIFR (retd)

Title: Gerbes and their cohomology classes

Abstract: After recalling the basics of gerbs and the morphisms between them, we will visit the following correspondences. Let F be a sheaf of abelian groups on a base X (in ordinary general topology, or in any subcanonical Grothendieck topology). Then there are the following natural isomorphisms. (0) The group of all global sections of F over X is isomorphic to the 0th cohomology of X with coefficients F. (1) The group of all isomorphism classes of F-torsors over X is isomorphic to the 1st cohomology of X with coefficients F. (2) The group of all isomorphism classes of F-gerbes on X is isomorphic to the 2nd cohomology of X with coefficients F. After briefly recalling (0) and (1), we will focus on (2). When X is a scheme with etale topology, and F is the sheaf G_m of invertible regular functions, the Brauer invariant of a sheaf of Azumaya algebras gives an illustration of the correspondence (2) in etale cohomology.

Description

Ramanujan Hall, Department of Mathematics

Date

Mon, December 11, 2023

Start Time

11:30am IST

Priority

5-Medium

Access

Public

Created by

DEFAULT ADMINISTRATOR

Updated

Sun, December 10, 2023 11:51pm IST