Algebraic Geometry Seminar
Tuesday, 30 January 2024, 11:30 am
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Host: Sudarshan Gurjar
Venue: Ramanujan Hall
Speaker: Nitin Nitsure
Affiliation: Bhaskaracharya Pratishthana, Pune
Title: Separated and proper morphisms of schemes
Abstract: The lecture will begin with closed and universally closed morphisms of schemes. We will prove, following B Poonen, that any scheme that is universally closed over Spec k (where k is any field) is quasi-compact. This will be followed by some basics of quasi-compact morphisms, preparing the way to study separated and proper morphisms via specialization of points. The lecture will be easily accessible to students that have looked at section 4 of Chapter 2 of Hartshorne's “Algebraic Geometry”