University of Münster
CRIS@UM
DE | EN

Frobenius homomorphisms in higher algebra

Basic data for this talk

Type of talk: scientific talk
Name der Vortragenden: Nikolaus, Thomas
Date of talk: 11/07/2022
Talk language: English
DOI: 10.4171/ICM2022/?
URL of slides: https://www.uni-muenster.de/IVV5WS/WebHop/user/nikolaus/Files/ICM_Slides.pdf

Information about the event

Name of the event: International Congress of Mathematics 2022
Event period: 06/07/2022 - 14/07/2022
Event location: Virtual event
Event website: https://www.mathunion.org/icm/virtual-icm-2022

Abstract

We will discuss versions of the Frobenius homomorphism for a ring spectrum R: the Tate- valued Frobenius R → RtCp and the Frobenius on topological Hochschild homology THH(R) → THH(R)tCp . Similar to ordinary algebra, these morphism play an impor- tant role in higher algebra and are related to various concepts in stable homotopy theory and algebraic K-theory. We discuss the notion of perfectness, which is to say that these morphisms are equivalences, and relate this notion to the Segal conjecture, the red-shift conjecture and the classification of spaces by stable data
Keywords: Frobenius homomorphisms

Speakers from the University of Münster

Nikolaus, Thomas
Professorship for theoretical mathematics (Prof. Nikolaus)