**Lecture series on algebraic stacks**

Monday 30 October, 11.30 am

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**Venue:** Ramanujan Hall

**Host:** Sudarshan Gurjar

**Speaker:** Nitin Nitsure

**Affiliation:** TIFR, Mumbai (Retd)

**Title:** The classifying stack BG for an algebraic group

**Abstract:** To any Lie group, there is classically associated a topological space BG with the requisite universal property in the homotopy category of paracompact topological spaces. For example, for G = GL(n) the space BG is the infinite Grassmannian. However, when we go to the algebraic category (say schemes or algebraic spaces and their morphisms), such a space BG does not exist. This is a paradigmatic example where algebraic stacks rescue the situation. In this lecture, we will explain the construction of an algebraic stack BG which has the requisite universal property of classifying principal G-bundles, where G is an algebraic group. The algebraic cohomology of this stack gives the algebraic cohomological version of the characteristic classes of principal G-bundles.