Seminar

Postdoc day, Seminar 4: Galois descent in topological Hochschild homology

Higher algebraic structures in algebra, topology and geometry

18 February 15:50 - 16:20

Maxime Ramzi - University of Copenhagen

Topological Hochschild homology (THH) is an interesting invariant of rings, related among other things to algebraic K-theory. One of its key properties is étale descent, which implies that one can work étale-locally to understand it. On the other hand, Rognes introduced in 2005 a theory of Galois extensions for ring spectra. Despite the name, Galois extensions of ring spectra are typically not étale, and in particular one can wonder independently of étale descent, whether THH satisfies Galois descent. This has been in part studied by Akhil Mathew, who gave a counterexample to the general statement, but also gave some examples where it is satisfied. In this talk, I will briefly introduce these objects and questions, and I will present a general criterion under which Galois descent holds in THH. This concrete criterion, stated in terms of separability, recovers some of the chromatic examples that Akhil obtained in joint work with Clausen, Naumann and Noel using more sophisticated ttechniques of "chromatic descent".

 

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Organizers
Gregory Arone
Stockholm University
Tilman Bauer
KTH Royal Institute of Technology
Alexander Berglund
Stockholm University
Søren Galatius
University of Copenhagen
Jesper Grodal,
University of Copenhagen
Thomas Kragh
Uppsala University

Program
Contact

Alexander Berglund

alexb@math.su.se

Søren Galatius

galatius@math.ku.dk

Thomas Kragh

thomas.kragh@math.uu.se

Other
information

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