Equivariant Euler characteristics and sheaf resolvents
For certain tame abelian covers of arithmetic surfaces we obtain formulas, involving a quadratic form derived from intersection numbers, for the equivariant Euler characteristics of both the canonical sheaf and also its square root. These formulas allow us to carry out explicit calculations; in particular, we are able to exhibit examples where these two Euler characteristics and that of the structure sheaf are all different and non-trivial. Our results are obtained by using resolvent techniques...