no. 6
Equivariant Euler characteristics and sheaf resolvents
[Caractéristiques d’Euler équivariantes et faisceau résolvant.]
Cassou-Noguès, Ph.1 ; Taylor, M.J.2
1 Institut de Mathématiques de Bordeaux Université Bordeaux 1 351, cours de la Libération 33405 Talence Cedex France
2 The University of Manchester School of Mathematics Alan Turing Building Oxford Road Manchester, M13 9PL UK
Annales de l'Institut Fourier, Tome 62 (2012) no. 6, pp. 2315-2345.

Nous obtenons pour certains revêtements modérés de surfaces arithmétiques des expressions des caractéristiques d’Euler équivariantes du faisceau canonique et de sa racine carrée qui font apparaître une forme quadratique décrite en terme de nombres d’intersection. Ces formules se prêtent au calcul. Elles nous permettent notamment de donner des exemples où ces caractéristiques ainsi que celle du faisceau structural sont deux à deux distinctes et non triviales. Nos résultats s’obtiennent par l’utilisation du théorème de Riemann-Roch local et par un calcul de résolvantes.

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 together with the local Riemann-Roch Theorem.

DOI : 10.5802/aif.2750
Classification : 11R04, 14C40
Keywords: Euler characteristic, resolvent, intersection numbers.
Mot clés : caratéristique d’Euler, résolvante, nombre d’intersection.

Cassou-Noguès, Ph. 1 ; Taylor, M.J. 2

1 Institut de Mathématiques de Bordeaux Université Bordeaux 1 351, cours de la Libération 33405 Talence Cedex France
2 The University of Manchester School of Mathematics Alan Turing Building Oxford Road Manchester, M13 9PL UK 
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Cassou-Noguès, Ph.; Taylor, M.J. Equivariant Euler characteristics and sheaf resolvents. Annales de l'Institut Fourier, Tome 62 (2012) no. 6, pp. 2315-2345. doi : 10.5802/aif.2750. https://aif.centre-mersenne.org/articles/10.5802/aif.2750/

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