Lecture series on algebraic stacks
Monday, 06 Nov 2023, 11:30 am
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Host: Sudarshan Gurjar
Venue: Ramanujan Hall
Speaker: Nitin Nitsure
Title: Schematic loci of algebraic spaces.
Abstract: Michael Artin showed that any algebraic space has a unique largest open subscheme which is dense in it. In this talk, we will give a proof. The ingredients of the proof are of even more general interest: the chief one is Grothendieck's form of Zariski's main theorem. The other inputs are the Grothendieck-Gabriel quotient theorem and a typical use of generic points of schemes. The lecture will focus on conceptual explanations, relegating the detailed proof to notes in the form of a handout for the participants.