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Une formule de Riemann-Roch équivariante pour les courbes

  • Niels Borne (a1)
Abstract

Soit G un groupe fini agissant sur une courbe algébrique projective et lisse X sur un corps algébriquement clos k. Dans cet article, on donne une formule de Riemann-Roch pour la caractéristique d'Euler équivariante d'un G-faisceau inversible ℒ, à valeurs dans l'anneau Rk (G) des caractères du groupe G. La formule donnée a un bon comportement fonctoriel en ce sens qu'elle relève la formule classique le long du morphisme dim: Rk (G) → ℤ, et est valable même pour une action sauvage. En guise d'application, on montre comment calculer explicitement le caractère de l'espace des sections globales d'une large classe de G-faisceaux inversibles, en s'attardant sur le cas particulier délicat du faisceau des différentielles sur la courbe.

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References
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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