Dans cet article on donne une formule explicite pour le caractère de Chern reliant la - 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.
In this paper we give an explicit formula for the Chern character from algebraic - 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.
Classification : 19D55, 16E40, 18H10, 19D45, 19C20
Mots clés : homologie cyclique, -théorie algébrique, caractère de Chern, symboles de Steinberg, symboles de Loday
@article{AIF_2004__54_7_2327_0, author = {Ginot, Gr\'egory}, title = {Formules explicites pour le caract\`ere de {Chern} en $K$-th\'eorie alg\'ebrique}, journal = {Annales de l'Institut Fourier}, pages = {2327--2355}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {54}, number = {7}, year = {2004}, doi = {10.5802/aif.2081}, zbl = {1068.19005}, mrnumber = {2139695}, language = {fr}, url = {http://www.numdam.org/articles/10.5802/aif.2081/} }
TY - JOUR AU - Ginot, Grégory TI - Formules explicites pour le caractère de Chern en $K$-théorie algébrique JO - Annales de l'Institut Fourier PY - 2004 DA - 2004/// SP - 2327 EP - 2355 VL - 54 IS - 7 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2081/ UR - https://zbmath.org/?q=an%3A1068.19005 UR - https://www.ams.org/mathscinet-getitem?mr=2139695 UR - https://doi.org/10.5802/aif.2081 DO - 10.5802/aif.2081 LA - fr ID - AIF_2004__54_7_2327_0 ER -
Ginot, Grégory. Formules explicites pour le caractère de Chern en $K$-théorie algébrique. Annales de l'Institut Fourier, Tome 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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