Jan 23, 2025
Atiyah-Segal completion theorem for singular varieties
Algebraic Geometry and Number Theory Seminar
Date: January 23, 2025 |
1:00 pm –
3:00 pm
Speaker:
Vladimir Sosnilo, University of Regensburg
Location: Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101)
Language:
English
We prove the AS completion theorem for almost toric actions on singular varieties in characteristic 0.
The strategy is based on the two ingredients:
1. the A1-invariant AS completion theorem proved by Amalendu Krishna;
2. a completion theorem for Hochschild homology proved by Harrison Chen.
To get the result the two ingredients are combined using the cyclotomic trace techniques.
As an application, we construct a complete motivic filtration on the AS completion of the equivariant K-theory, extending Elmanto-Morrow filtration from the case of schemes.
This is based on joint work in progress with Elden Elmanto and Dmitry Kubrak.
