23. Jan 2025

Atiyah-Segal completion theorem for singular varieties

Algebraic Geometry and Number Theory Seminar

Datum: 23. January 2025 | 13:00 – 15:00
Sprecher: Vladimir Sosnilo, University of Regensburg
Veranstaltungsort: Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101)
Sprache: Englisch

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.