Frobenius homomorphisms in higher algebra
Thomas Nikolaus
FB Mathematik und Informatik, Universität Münster, Einsteinstr. 62, D-48149 Münster, Germany
![Frobenius homomorphisms in higher algebra cover](/_next/image?url=https%3A%2F%2Fcontent.preview.ems.press%2Fassets%2Fpublic%2Fimages%2Fbooks%2Fcover-276.png&w=3840&q=90)
Download Chapter PDF
This book chapter is published open access.
Abstract
We will discuss versions of the Frobenius homomorphism for a ring spectrum : the Tate-valued Frobenius and the Frobenius on topological Hochschild homology . Similar to ordinary algebra, these morphisms play an important role in higher algebra and are related to various concepts in stable homotopy theory and algebraic -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.