Ivan Arzhantsev to speak on 'Quotients by Algebraic Group Actions'

On September 24, 2025, Ivan Arzhantsev, Dean of the Faculty of Computer Science, will deliver a report on 'Quotients by Algebraic Group Actions' at the seminar of the Laboratory on Algebraic Transformation Groups.

Abstract:

We present different concepts of quotients including rational, categorical, geometric and good quotients. Starting with the set-theoretical approach and Rosenlicht’s theorem, we come to the quotient of a reductive group action on an affine variety along with possible generalizations. We discuss Mumford’s  construction of the quotient of the set of semistable points defined by a G-linearized line bundle and variations of GIT quotients. We explain how quotient constructions motivate the study of certain extensions of the category of algebraic varieties.

Time: 18:00

Place: 11 Pokrovsky Bulvar, room G108.