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Number Theory Seminar
Seminar information archive ～05/02｜Next seminar｜Future seminars 05/03～
| Date, time & place | Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Naoki Imai, Shane Kelly |
2024/10/30
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Masaya Sato (University of Tokyo)
Representability of Hochschild homology in the category of motives with modulus (日本語)
Masaya Sato (University of Tokyo)
Representability of Hochschild homology in the category of motives with modulus (日本語)
[ Abstract ]
There is a map from algebraic K-theory to Hochschild homology, called a trace map. This map developed the study of algebraic K-theory. Algebraic K-theory is A^1-invariant on the category of smooth schemes over a field, so the Voevodsky’s motivic homotopy theory is a nice way to study algebraic K-theory. However, Hochschild homology is not A^1-invariant, so Voevodsky’s theory doesn’t capture it. In this talk, we will extend Hochschild homology of schemes to modulus pairs, and it is representable in the category of motives with modulus defined by Kahn-Miyazaki-Saito-Yamazaki.
There is a map from algebraic K-theory to Hochschild homology, called a trace map. This map developed the study of algebraic K-theory. Algebraic K-theory is A^1-invariant on the category of smooth schemes over a field, so the Voevodsky’s motivic homotopy theory is a nice way to study algebraic K-theory. However, Hochschild homology is not A^1-invariant, so Voevodsky’s theory doesn’t capture it. In this talk, we will extend Hochschild homology of schemes to modulus pairs, and it is representable in the category of motives with modulus defined by Kahn-Miyazaki-Saito-Yamazaki.
