Logarithmic Hochschild homology

Abstract

The purpose of this thesis is to analyse the logarithmic Hochschild homology for pre-log rings and to provide some tools to compute it in certain cases. One of the main strategies that we will employ to describe the log Hochschild homology will entail passing through the module of the log Kahler differentials. An additional technique that we can adopt to gather information about the log Hochschild homology of some specific pre-log rings is to interlock it in a long exact sequence, relating it to the ordinary Hochschild homology groups. An example in which this method applies nicely is the case where the remaining terms of the long exact sequence are the Hochschild homology of polynomial algebras in a finite number of variables, for which we try to provide an exhaustive description.