Polygons and TR with coefficients

Speaker: Jonas McCandless - University of Münster

Abstract: I will introduce the notion of a polygonic spectrum which is a multi-object version of the notion of a cyclotomic spectrum indexed by polygons rather than the circle. This is designed to capture the structure on topological Hochschild homology of a ring with coefficients in a bimodule. Using this, I will explain the construction of TR with coefficients and explain how this is equipped with compatible Frobenius and Verschiebung maps. Time permitting, I will discuss the relation to Bloch’s spectrum of curves on algebraic K-theory. This is based on joint work with Achim Krause and Thomas Nikolaus.