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Abstract: For certain tame abelian covers of arithmetic surfaces X-Y we obtain strikingformulas, involving a quadratic form derived from intersection numbers, for theequivariant Euler characteristics of both the canonical sheaf !X-Y and also itssquare root !1-2 X-Y . These formulas allow us us to carry out explicitcalculations; in particular, we are able to exhibit examples where these twoEuler characteristics and that of the the structure sheaf of X are alldifferent and non-trivial. Our results are obtained by using resolventtechniques together with the local Riemann-Roch approach developed in CPT.



Author: Ph. Cassou-Nogu`es, M.J. Taylor

Source: https://arxiv.org/



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