Higher Epsilon Factors ("HEF")


This is the public webpage for the EU-funded project "Higher Epsilon factors". The research presented here was by performed by Michael Groechenig and collaborators during his time (October 2016 - June 2018) as a Marie Skłodowska-Curie fellow at FU Berlin, as a member of the group of Prof. Esnault.

The content of this project lies in the transition zone between algebra and analysis. It is concerned with the study of systems of differential equations (as they arrive in algebraic geometry) from an arithmetic perspective. This leads to a mix of algebraic, categorical and analytical methods and sheds new light on the structures governing differential equations (that is, holonomic D-modules on algebraic varieties, Higgs bundles, F-isocrystals).


The results of the research carried out during the duration of this project are described in the following articles:

De Rham epsilon factors for flat connections on higher local fields Higher de Rham epsilon factors On the normally ordered tensor product and duality for Tate objects
(joint with Braunling, Wolfson and Heleodoro)
Cohomologically rigid local systems and integrality
(joint with Esnault)
Rigid connections and F-isocrystals
(joint with Esnault)
Mirror symmetry for moduli spaces of Higgs bundles via p-adic integration
(joint with Wyss and Ziegler)

An introduction to de Rham epsilon factors (not intended to be published).

   This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 701679.