Geodesic
On Grothendieck group of simply connected semisimple algebraic groups
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 13, Tome 330 (2006), pp. 223-235 
O. B. Podkopaev. On Grothendieck group of simply connected semisimple algebraic groups. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 13, Tome 330 (2006), pp. 223-235. http://geodesic.mathdoc.fr/item/ZNSL_2006_330_a11/
@article{ZNSL_2006_330_a11,
     author = {O. B. Podkopaev},
     title = {On {Grothendieck} group of simply connected semisimple algebraic groups},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {223--235},
     year = {2006},
     volume = {330},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_330_a11/}
}
TY  - JOUR
AU  - O. B. Podkopaev
TI  - On Grothendieck group of simply connected semisimple algebraic groups
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2006
SP  - 223
EP  - 235
VL  - 330
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2006_330_a11/
LA  - ru
ID  - ZNSL_2006_330_a11
ER  - 
%0 Journal Article
%A O. B. Podkopaev
%T On Grothendieck group of simply connected semisimple algebraic groups
%J Zapiski Nauchnykh Seminarov POMI
%D 2006
%P 223-235
%V 330
%U http://geodesic.mathdoc.fr/item/ZNSL_2006_330_a11/
%G ru
%F ZNSL_2006_330_a11

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The $K_0$ groups of simply connected semisimple algebraic groups are calculated. The triviality of Chow groups $CH^1$ and $CH^2$ of such groups is obtained as a corollary.

[1] A. Borel, Lineinye algebraicheskie gruppy, Mir, M., 1972 | MR | Zbl

[2] N. Burbaki, Algebra: moduli, koltsa, formy, Nauka, M., 1966 | MR

[3] V. E. Voskresenskii, Algebraicheskie tory, Nauka, M., 1977 | MR

[4] D. Quillen, “Higher algebraic $K$-theory, I”, Lect. Notes Math., 341, Springer-Verlag, Berlin et al., 1973, 85–147 | MR

[5] A. S. Merkurev, “Sravnenie ekvivariantnoi i obyknovennoi $K$-teorii algebraicheskikh mnogoobrazii”, Algebra i analiz, 9:4 (1997), 175–214 | MR

[6] Dzh. Miln, Etalnye kogomologii, Mir, M., 1983 | MR

[7] I. A. Panin, “On the algebraic $K$-theory of twisted flag varieties”, $K$-Theory, 8 (1994), 541–585 | DOI | MR | Zbl

[8] I. A. Panin, “Printsip rasschepleniya i $K$-teoriya odnosvyaznykh poluprostykh algebraicheskikh grupp”, Algebra i analiz, 10:1 (1998), 88–131 | MR | Zbl

[9] V. P. Platonov, A. S. Rapinchuk, Algebraicheskie gruppy i teoriya chisel, Nauka, M., 1991 | MR

[10] Zh. P. Serr, Kogomologii Galua, Mir, M., 1968 | MR

[11] R. Thomason, “Algebraic $K$-theory of group scheme actions”, Algebraic Topology and Algebraic $K$-theory (Princeton, NJ, 1983), Princeton Univ. Press, Princeton, NJ, 1987, 539–563 | MR | Zbl

[12] Dzh. Khamfri, Lineinye algebraicheskie gruppy, Nauka, M., 1980 | MR

[13] J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer-Verlag, Berlin et al., 1972 | MR | Zbl

[14] C. Scheiderer, Real and Étale Cohomology, Springer-Verlag, Berlin et al., 1994 | MR | Zbl