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.
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.
Mot clés : homologie cyclique, $K$-théorie algébrique, caractère de Chern, symboles de Steinberg, symboles de Loday
Keywords: Cyclic homology, algebraic $K$-theory, Chern character, Steinberg symbols, Loday Symbols
Ginot, Grégory 1
@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 = {https://aif.centre-mersenne.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 SP - 2327 EP - 2355 VL - 54 IS - 7 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2081/ DO - 10.5802/aif.2081 LA - fr ID - AIF_2004__54_7_2327_0 ER -
%0 Journal Article %A Ginot, Grégory %T Formules explicites pour le caractère de Chern en $K$-théorie algébrique %J Annales de l'Institut Fourier %D 2004 %P 2327-2355 %V 54 %N 7 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2081/ %R 10.5802/aif.2081 %G fr %F AIF_2004__54_7_2327_0
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. https://aif.centre-mersenne.org/articles/10.5802/aif.2081/
[1] Cohomology of groups, Graduate Texts in Mathematics, 87, Springer-Verlag, New York-Berlin, 1982 | MR | Zbl
[2] -structures in algebraic -theory and cyclic homology, -Theory, Volume 4 (1990-1991) no. 6, pp. 591-606 | DOI | MR | Zbl
[3] Noncommutative differential geometry, I, II, Publ. Math. Inst. Hautes Étud. Sci, Volume 62 (1985), pp. 41-144 | DOI | EuDML | Numdam | MR | Zbl
[4] Differentials in algebraic -theory (1975) (non publié, circa)
[5] Algebraic -theory and Hochschild homology (1975-1976) (non publié)
[6] of discrete valuation rings, Advances in Math, Volume 18 (1975) no. 2, pp. 182-238 | DOI | MR | Zbl
[7] Free differential calculus. I. Derivation in the free group ring, Ann. of Math. (2), Volume 57 (1953), pp. 547-560 | DOI | MR | Zbl
[8] Produit tensoriel de matrices, homologie cyclique, homologie des algèbres de Lie, Ann. Inst. Fourier, Grenoble, Volume 44 (1994) no. 2, pp. 413-431 | DOI | EuDML | Numdam | MR | Zbl
[9] Hodge decompositions of Loday symbols in -theory and cyclic homology, -Theory, Volume 8 (1994) no. 6, pp. 587-632 | DOI | MR | Zbl
[10] Relative algebraic -theory and cyclic homology, Ann. of Math. (2), Volume 124 (1986) no. 2, pp. 347-402 | DOI | MR | Zbl
[11] Some algebraic properties of cyclic homology groups, -Theory, Volume 1 (1987) no. 4, pp. 361-384 | DOI | MR | Zbl
[12] Cyclic homology and equivariant homology, Invent. Math, Volume 87 (1987), pp. 403-424 | DOI | EuDML | MR | Zbl
[13] Adams operations and the Dennis trace map, J. Pure Appl. Algebra, Volume 144 (1999) no. 1, pp. 21-27 | DOI | MR | Zbl
[14] Homologie cyclique et -théorie, Astérisque, 149, Soc. Math. France, Paris, 1987 | MR | Zbl
[15] Cyclic homology, comodules, and mixed complexes, J. Algebra, Volume 107 (1987) no. 1, pp. 195-216 | DOI | MR | Zbl
[16] Homologie cyclique, caractère de Chern et lemme de perturbation, J. Reine Angew. Math, Volume 408 (1990), pp. 159-180 | DOI | EuDML | MR | Zbl
[17] -structure en -théorie algébrique, Comment. Math. Helv, Volume 55 (1980) no. 2, pp. 233-254 | DOI | EuDML | MR | Zbl
[18] -théorie algébrique et représentations de groupes, Ann. Sci. École Norm. Sup. (4), Volume 9 (1976) no. 3, pp. 309-377 | EuDML | Numdam | MR | Zbl
[19] Symboles en -théorie algébrique supérieure, C. R. Acad. Sci. Paris, Sér. I Math., Volume 292 (1981) no. 18, pp. 863-866 | MR | Zbl
[20] Cyclic homology, Springer-Verlag, Berlin, 1998 | MR | Zbl
[21] Cyclic homology and lambda operations (NATO Adv. Sci. Inst. Sér. C, Math. Phys. Sci.), Volume 279 (1989), pp. 209-224 | Zbl
[22] Cyclic homology and the Lie algebra homology of matrices, Comment. Math. Helv, Volume 59 (1984) no. 4, pp. 569-591 | EuDML | MR | Zbl
[23] A presentation for of split radical pairs, J. Pure Appl. Algebra, Volume 10 (1977/78) no. 3, pp. 271-294 | DOI | MR | Zbl
[24] The cyclic homology of an exact category, J. Pure Appl. Algebra, Volume 93 (1994) no. 3, pp. 251-296 | DOI | MR | Zbl
[25] Introduction to algebraic -theory, Annals of Mathematics Studies, Princeton University Press and University of Tokyo Press, Princeton, N.J. and Tokyo, 1971 | MR | Zbl
[26] Generating the tame and wild kernels by Dennis-Stein symbols, -Theory, Volume 5 (1991/92) no. 5, pp. 449-470 | DOI | MR | Zbl
[27] Éléments cyclotomiques en -théorie (Astérisque) (1987), pp. 147-148 | Zbl
[28] Homology of matrix algebras over rings and Hochschild homology, Uspekhi Mat. Nauk, Volume 38 (1983), pp. 217-218 | MR | Zbl
[28] Homology of matrix algebras over rings and Hochschild homology, Russ. Math. Surveys, Volume 38 (1983), pp. 198-199 | DOI | MR | Zbl
[29] Nil -theory maps to cyclic homology, Trans. Amer. Math. Soc, Volume 303 (1987) no. 2, pp. 541-558 | MR | Zbl
[30] An introduction to algebraic -theory (, http://math.rutgers.edu:80/weibel/Kbook.html)
Cited by Sources: