Equivariant Euler characteristics and sheaf resolvents
Cassou-Nogu`es, Ph. · Taylor, M. J.
Original · EN
For certain tame abelian covers of arithmetic surfaces X/Y we obtain striking formulas, involving a quadratic form derived from intersection numbers, for the equivariant Euler characteristics of both the canonical sheaf!X/Y and also its square root!1/2 X/Y. These formulas allow us us to carry out explicit calculations; in particular, we are able to exhibit examples where these two Euler characteristics and that of the the structure sheaf of X are all different and non-trivial. Our results are obtained by using resolvent techniques together with the local Riemann-Roch approach developed in [CPT].
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