K-théorie pour les singularités coniques isolées

For a compact singular variety with isolated conical singularities we define K-theory groups which depend upon a non-negative integer less than the dimension. In the rational setting, the null case gives the K-theory of the singular variety, the biggest case gives the K-theory of the manifold with boundary obtained when excising the singular points. We define also a Chern character which takes its values in the intersection cohomology associated to a suitable perversity. This character is an isomorphism in the rational setting. We give a Chern-Weil version of the above constructions using the multiplicative K-theory of Karoubi. To cite this article: A. Legrand, D. Poutriquet, C. R. Acad. Sci. Paris, Ser. I 341 (2005).