Tuesday 5 April 2022, 16:00 - 17:00 in HG03.082
Tommy Lundemo (RU)
A logarithmic Hochschild-Kostant-Rosenberg theorem
The Hochschild-Kostant-Rosenberg theorem relates the de Rham complex of smooth algebras to Hochschild homology. The latter is an invariant of commutative rings which appears frequently in representation theory, (derived) algebraic geometry, and homotopy theory. In all of these contexts, the HKR-theorem plays a central role in the study and applications of Hochschild homology.
Logarithmic geometry is a variant of algebraic geometry in which the notion of smoothness is more flexible. John Rognes has extended the definition of Hochschild homology to allow for log rings - the affine schemes of log geometry - as input. I will motivate and state a version of the HKR-theorem in this context. If time permits, I will briefly explain a version of this result in the context of stable homotopy theory.
This is joint work with Federico Binda, Doosung Park, and Paul Arne Østvær.