Morten Brun

"Hochschild-Witt homology"

Abstract: I will describe a homology theory for associative algebras that is related to the de Rham-Witt complex in a way analog to the way Hochschild holology is related to the de Rham complex. There is a trace map from K-theory to Hochschild-Witt homology factoring through topological cyclic homology. It is possible to construct an approximation to topological cyclic homology out of Hochschild-Witt holology. The difference between topological cyclic homology and this approximation is of the same nature as the difference between topological Hochschild homology and Hochschild homology.