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Comptes Rendus Mathématique
Volume 338, n° 1
pages 41-46 (janvier 2004)
Doi : 10.1016/j.crma.2003.10.005
Received : 13 February 2003 ;  accepted : 7 October 2003
Interprétation motivique de la formule d'excès d'intersection
Motivic interpretation of the excess intersection formula

Frédéric  Déglise
Institut de mathématique, Université Paris 7, 175, rue du Chevaleret, 75013 Paris, France 

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Suivant Voevodsky, on sait associer un triangle de Gysin dans la catégorie des motifs triangulés à tout couple   formé d'un schéma lisse   et d'un sous-schéma fermé lisse   de  . Nous étudions la fonctorialité de ce triangle de Gysin : si l'on se donne un morphisme   transverse à  , cette fonctorialité est simple. Nous nous intéressons au cas où le morphisme   n'est pas tout à fait transverse à  , obtenant ainsi une formule motivique d'excès d'intersection et une formule qui fait intervenir la ramification au sens des anneaux de valuations discrètes d'égale caractéristique. Pour citer cet article : F. Déglise, C. R. Acad. Sci. Paris, Ser. I 338 (2004).

Abstract

Following Voevodsky, one can associate a Gysin triangle in the category of triangulated motives to every couple   such that   is a smooth scheme and   is a smooth closed subscheme of  . We study the functoriality of this triangle: if one considers a morphism   which is transversal to  , this functoriality is simple. We are rather interested in the case where   is not quite transversal to  . In that case, one obtains a motivic excess intersection formula and a ramification formula in the sense of equicharacteristic discrete valuation rings. To cite this article: F. Déglise, C. R. Acad. Sci. Paris, Ser. I 338 (2004).




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