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

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.