Trace theories and their uses

Dmitry Kaledin (Higher School of Economics)

Wednesday 8th May 15:00-16:00 Maths 116

Abstract

It is now well-understood that many interesting cohomology theories in algebraic geometry are in fact non-commutative in nature, and should be understood as localizing invariants of DG-categories. For 
example, differential forms are just Hochschild Homology classes. However, this point of view ingores one important feature of Hochschild Homology: it is a theory with two parameters, an algebra and a bimodule. It turns out that you can sometimes trade one for another, and extract general results from the particular case when the algebra is just the base field (but the bimodule is arbitrary). I am going to describe the formalism of "trace theories" that accomplishes this. If time permits, I will also give some applications to Topological Hochschild Homology.

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