4 papers
Traces, Schubert calculus, and Hochschild cohomology of category
Clemens Koppensteiner
We discuss how the Hochschild cohomology of a dg category can be computed as the trace of its Serre functor. Applying this approach to the principal block of the Bernstein--Gelfand…
Graded topological spaces
Clemens Koppensteiner
We introduce the notion of a "graded topological space": a topological space endowed with a sheaf of abelian groups which we think of as a sheaf of gradings. Any object living on a…
The de Rham functor for logarithmic D-modules
Clemens Koppensteiner
In the first part we deepen the six-functor theory of (holonomic) logarithmic D-modules, in particular with respect to duality and pushforward along projective morphisms. Then, ins…
Holonomic and perverse logarithmic D-modules
Clemens Koppensteiner, Mattia Talpo
We introduce the notion of a holonomic D-module on a smooth (idealized) logarithmic scheme and show that Verdier duality can be extended to this context. In contrast to the classic…