Lecture series on algebraic stacks
Friday, 15 September, 11:30 am
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Venue: Ramanujan Hall
Host: Sudarshan Gurjar
Speaker : Nitin Nitsure
Affiliation: TIFR, Mumbai (retd)
Title: Fibered groupoids and stacks.
Abstract: Schemes can be understood via their functors of points. Descent theory shows that these functors are big etale sheaves over Spec Z. Amongst such sheaves, schemes and algebraic spaces are characterized by further 'algebraicity' conditions. Similarly, algebraic stacks are fibered groupoids which are stacks, which are the analogue of the sheaf and descent conditions. A further 'algebraicity' condition defines algebraic stacks. In the next few lectures, we will look at fibered groupoids and stacks, and give many examples. This will prepare the ground for introducing the algebraicity conditions that characterize algebraic stacks.