Geodesic
Leibniz formula in algebraic $K$-theory
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 11, Tome 319 (2004), pp. 264-292 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The paper can be considered as an addendum to a paper of Thomason and Throbaugh where $K$-theory of algebraic varieties is equipped with relative $K$-groups. It is proved that this enriched $K$-theory satisfies the Panin–Smirnov axioms for ring cohomology theories of algebraic varieties. In particular it is proved that the Leibnitz formula, describing an interaction between a multiplication and a differential, holds in this case. A language of symmetric spectra and of monoidal model categories is used. 
@article{ZNSL_2004_319_a9,
     author = {A. L. Smirnov},
     title = {Leibniz formula in algebraic $K$-theory},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {264--292},
     year = {2004},
     volume = {319},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_319_a9/}
}
TY  - JOUR
AU  - A. L. Smirnov
TI  - Leibniz formula in algebraic $K$-theory
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2004
SP  - 264
EP  - 292
VL  - 319
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2004_319_a9/
LA  - ru
ID  - ZNSL_2004_319_a9
ER  - 
%0 Journal Article
%A A. L. Smirnov
%T Leibniz formula in algebraic $K$-theory
%J Zapiski Nauchnykh Seminarov POMI
%D 2004
%P 264-292
%V 319
%U http://geodesic.mathdoc.fr/item/ZNSL_2004_319_a9/
%G ru
%F ZNSL_2004_319_a9
A. L. Smirnov. Leibniz formula in algebraic $K$-theory. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 11, Tome 319 (2004), pp. 264-292. http://geodesic.mathdoc.fr/item/ZNSL_2004_319_a9/

[1] I. Panin, A. Smirnov, Push-forwards in oriented cohomology theories of algebraic varieties, K-theory Preprint Archives, 459, 2000

[2] R. Thomason, T. Throbaugh, “Higher algebraic K-theory of schemes and of derived categories”, The Grothendieck Festschrift, 3, Birkhäuser, Boston, 1990, 247–435 | MR | Zbl

[3] Th. Geisser, L. Hesselholt, Topological cyclic homology of schemes, K-theory Preprint Archives, 231, 1997 | MR

[4] M. Hovey, Model categories, Mathematical Surveys and Monographs, 63, AMS, 1999, 209 | MR | Zbl

[5] M. Hovey, B. Shipley, J. Smith, Symmetric spectra, K-theory Preprint Archives, 265, 1998 | MR

[6] A. Borel, J. P. Serre, “Le théorème de Riemann–Roch”, Bull. Soc. Math. France, 86 (1958), 97–136 | MR | Zbl

[7] F. Waldhausen, “Algebraic $K$-theory of spaces”, Lect. Notes Math., 1126, 1985, 318–419 | MR | Zbl