Formules explicites pour le caractère de Chern en $K$-théorie algébrique

Ginot, Grégory

doi:10.5802/aif.2081

Formules explicites pour le caractère de Chern en

K

-théorie algébrique
[Explicit formulas for the Chern character in algebraic

K

-theory]

Ginot, Grégory ¹

¹ Université Paris 13, ENS Cachan, CMLA-LAGA, 61 avenue du Président Wilson, 94235 Cachan Cedex (France)

Annales de l'Institut Fourier, Volume 54 (2004) no. 7, pp. 2327-2355.

Abstract
Résumé

In this paper we give an explicit formula for the Chern character from algebraic $K$ - theory to negative cyclic homology. We compute formulas for the Chern character of Steinberg, Dennis-Stein and Loday symbols. From the previous results we get a new proof of the compatibility of the Chern character with products.

Dans cet article on donne une formule explicite pour le caractère de Chern reliant la $K$ - théorie algébrique et l’homologie cyclique négative. On calcule le caractère de Chern des symboles de Steinberg et de Loday et on donne une preuve élémentaire du fait que le caractère de Chern est multiplicatif.

MR: 2139695 | Zbl: 1068.19005

DOI: 10.5802/aif.2081

Classification: 19D55, 16E40, 18H10, 19D45, 19C20
Keywords: Cyclic homology, algebraic

K

-theory, Chern character, Steinberg symbols, Loday Symbols

Author's affiliations:

Ginot, Grégory ¹

¹ Université Paris 13, ENS Cachan, CMLA-LAGA, 61 avenue du Président Wilson, 94235 Cachan Cedex (France)

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     title = {Formules explicites pour le caract\`ere de {Chern} en $K$-th\'eorie alg\'ebrique},
     journal = {Annales de l'Institut Fourier},
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Ginot, Grégory. Formules explicites pour le caractère de Chern en $K$-théorie algébrique. Annales de l'Institut Fourier, Volume 54 (2004) no. 7, pp. 2327-2355. doi : 10.5802/aif.2081. http://www.numdam.org/articles/10.5802/aif.2081/

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