Vorträge des SFB 1442

Fontaine´s theory of (\varphi, \Gamma)-modules is a fundamental tool to describe and classify continuous representations of the Galois group. The following talk will present the results from the author's PhD dissertation, where a multivariable version of the category of (\phi, \Gamma)-modules is introduced. More exactly, we focus on étale (\phi, \Gamma)-modules over a multivariable Laurent power series ring over the ring of integers of a given local field. These modules classify the continuous representations of a n-fold product of the absolute Galois group of the local field with coefficients in the ring of integers.

This talk is about groupoids and C*-algebras generated by left regular representations of certain left cancellative small categories called Garside categories. I will explain these objects and constructions with the help of many concrete example classes. I will also give an overview of structural results for C*-algebras, groupoids and topological full groups arising from Garside categories.

The purpose of this talk is to introduce the notion of a polygonic spectrum which is a multi-object version of the notion of a cyclotomic spectrum indexed by the n-polygons rather than the circle. This is designed to capture the structure on topological Hochschild homology of a ring with coefficients in a bimodule. We obtain the polygonic structure on topological Hochschild homology by studying THH as a trace theory on a category of cyclic graphs whose vertices are labelled by rings and whose edges are labelled by bimodules. This provides a convenient formalism for expressing the cyclic invariance of THH and HH. The polygonic structure on THH with coefficients allows us to introduce a version of TR with coefficients. This is joint work with Achim Krause and Thomas Nikolaus.