Vol. 5, No. 1, 2020

Download this article
Download this article For screen
For printing
Recent Issues
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the Journal
Editorial Board
Ethics Statement
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 2379-1691 (e-only)
ISSN: 2379-1683 (print)
Author Index
To Appear
Other MSP Journals
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

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.

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
Received: 21 August 2018
Revised: 17 June 2019
Accepted: 7 August 2019
Published: 21 March 2020
Werner Bley
Mathematisches Institut
Ludwig-Maximilians-Universität München
David Burns
Department of Mathematics
King’s College London
United Kingdom
Carl Hahn
United Kingdom