Mathematics Seminars and Colloquia
4 December 2023- 9 December 2023
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Lecture series on algebraic stacks
Monday, 4th December, 11:30 am
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Host: Sudarshan Gurjar
Venue: Ramanujan Hall
Speaker: Nitin Nitsure, TIFR (retd)
Title: Gerbes and their cohomology classes
Abstract: Locally trivial fiber bundles can be described by their transition functions, giving a class in the first Cech cohomology of the structure group. Gerbes can be regarded as a `higher' version of this twisting phenomenon. The local description of a gerbe gives rise to a class in the second Cech cohomology of the base with coefficients in the `band' (lien in French) of the gerbe. This description of the cohomology class of a gerbe is particularly simple when the band is abelian, which is the case we will describe in this talk. The cohomological Brauer class of Azumaya algebra (or of a projective bundle) is an example of such a cohomological class.