Lecture series on algebraic stacks

Monday, 28 August, 11:30 am-1.00 pm

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Venue: Ramanujan Hall

Host: Sudarshan Gurjar

Speaker : Nitin Nitsure

Affiliation: TIFR, Mumbai (retd)

Title: Algebraic spaces-II

Abstract:  In his talk `The Implicit Function Theorem in Algebraic Geometry', delivered at the legendary conference `Algebraic Geometry, Bombay-1968', Michael Artin expanded the category of spaces used in algebraic geometry by introducing `algebraic spaces', which was a step beyond the schemes of Grothendieck. In the 55 years that have passed since then, algebraic spaces have become an important part of Algebraic Geometry. In particular, the theory of algebraic stacks makes foundational use of them.

In this lecture, we will introduce algebraic spaces, just assuming that the audience is familiar with schemes at the level of the first few sections of Chapter 2 of Hartshorne's textbook Algebraic Geometry'. After giving some motivation and examples, some basic properties of algebraic spaces will be outlined.

This lecture is the beginning of a series of about 12 talks titled `An Introduction to Algebraic Stacks'. The aim of this series is to cover the first half of the textbook `Champs Algebriques' by Laumon and Moret-Bailly. This knowledge is essential in order to follow a whole lot of modern research in both arithmetic and geometry.