Invariants Associated to Orthogonal $\epsilon$-constants

Abstract

In this paper we use the theory of $\epsilon$-constants associated to tame finite group actions on arithmetic surfaces to define a Brauer group invariant $μ(\X,G,V)$ associated to certain symplectic motives of weight one. We then discuss the relationship between this invariant and $w_2(\pi )$, the Galois theoretic invariant associated to tame covers of surfaces.

9 pages