Higher Epsilon-Factors for Higher Local Fields

Objetivo

The goal of this project is to extend the work of Beilinson-Bloch-Esnault (BBE) on de Rahm epsilon-factors in dimension one to higher local fields. Together with my collaborators Oliver Braunling and Jesse Wolfson we have carefully studied one of the main tools of BBE, Tate vector bundles, in an abstract context which allows to handle higher-dimensional situations. Moreover, we have successfully constructed a special case of higher epsilon-factors, called higher-dimensional Contou-Carrère symbols, and established an array of reciprocity laws for this case. It seems very likely that similar methods, also of K-theoretic nature like in the case of symbols, can be used to shed light on higher de Rahm epsilon-factors, and reciprocity phenomena thereof. The candidate will investigate the connection between the approach via Tate objects, and extend Patel's K-theoretic framework in a compatible way. A higher analogue of Beilinson's topological epsilon-factors is also envisioned, and a comparison result between this theory and the de Rham version. This project offers a new viewpoint on the arithmetic and geometric behaviour of higher local fields.