Vol. 5, No. 1, 2020

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On refined metric and hermitian structures in arithmetic, I: Galois–Gauss sums and weak ramification

Werner Bley, David Burns and Carl Hahn

Vol. 5 (2020), No. 1, 79–140
DOI: 10.2140/akt.2020.5.79
Abstract

We use techniques of relative algebraic K-theory to develop a common refinement of the theories of metrized and hermitian Galois structures in arithmetic. As a first application of the general approach, we then use it to prove several new results, and to formulate several explicit new conjectures, concerning the detailed arithmetic properties of a natural class of wildly ramified Galois–Gauss sums.

Keywords
Galois module structure, weakly and wildly ramified Galois–Gauss sums, relative algebraic $K$-theory, Galois–Jacobi sums
Mathematical Subject Classification 2010
Primary: 11R33, 16E20, 19A49
Milestones
Received: 21 August 2018
Revised: 17 June 2019
Accepted: 7 August 2019
Published: 21 March 2020
Authors
Werner Bley
Mathematisches Institut
Ludwig-Maximilians-Universität München
München
Germany
David Burns
Department of Mathematics
King’s College London
Strand
London
United Kingdom
Carl Hahn
London
United Kingdom