Central extensions of reductive groups by K 2
Publications Mathématiques de l'IHÉS, Tome 94 (2001), pp. 5-85.
@article{PMIHES_2001__94__5_0,
     author = {Brylinski, Jean-Luc and Deligne, Pierre},
     title = {Central extensions of reductive groups by $K_2$},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {5--85},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {94},
     year = {2001},
     mrnumber = {1896177},
     zbl = {1093.20027},
     language = {en},
     url = {http://archive.numdam.org/item/PMIHES_2001__94__5_0/}
}
TY  - JOUR
AU  - Brylinski, Jean-Luc
AU  - Deligne, Pierre
TI  - Central extensions of reductive groups by $K_2$
JO  - Publications Mathématiques de l'IHÉS
PY  - 2001
SP  - 5
EP  - 85
VL  - 94
PB  - Institut des Hautes Études Scientifiques
UR  - http://archive.numdam.org/item/PMIHES_2001__94__5_0/
LA  - en
ID  - PMIHES_2001__94__5_0
ER  - 
%0 Journal Article
%A Brylinski, Jean-Luc
%A Deligne, Pierre
%T Central extensions of reductive groups by $K_2$
%J Publications Mathématiques de l'IHÉS
%D 2001
%P 5-85
%V 94
%I Institut des Hautes Études Scientifiques
%U http://archive.numdam.org/item/PMIHES_2001__94__5_0/
%G en
%F PMIHES_2001__94__5_0
Brylinski, Jean-Luc; Deligne, Pierre. Central extensions of reductive groups by $K_2$. Publications Mathématiques de l'IHÉS, Tome 94 (2001), pp. 5-85. http://archive.numdam.org/item/PMIHES_2001__94__5_0/

[1] S. Bloch, Some formulas pertaining to the K-theory of commutative group schemes, J. Alg. 53 (1978), 304-326. | MR | Zbl

[2] S. Bloch, A note on Gersten's conjecture in the mixed characteristic case, in: Applications of algebraic K-theory to algebraic geometry and number theory (Boulder, 1983), Contemp. Math. 55, AMS (1986), 75-78. | Zbl

[3] S. Bloch and K. Kato, p-adic étale cohomology, Publ. Math. IHES 63 (1986), 107-152. | EuDML | Numdam | MR | Zbl

[4] S. Bloch and A. Ogus, Gersten's conjecture and the homology of schemes, Ann. Sci. Ec. Norm. Sup. 7 (1974), 181-202. | EuDML | Numdam | Zbl

[5] F. Bruhat et J. Tits, Groupes réductifs sur un corps local II, Publ. Math. IHES 60 (1984), 5-184. | EuDML | Numdam | MR | Zbl

[6] J. L. Brylinski and D. Mclaughlin, The geometry of the first Pontryagin class and of line bundles on loop spaces I, Duke Math. J. 35 (1994), 603-638. | MR | Zbl

[7] J.-L. Colliot-Thélène, Hilbert Theorem 90 for K2, with application to the Chow groups of rational surfaces, Invent. Math. 71 (1983), 1-20. | EuDML | MR | Zbl

[8] P. Deligne, Extensions centrales de groupes algébriques simplement connexes et cohomologie galoisienne, Publ. Math. IHES 84 (1996), 35-89. | EuDML | Numdam | MR | Zbl

[9] M. Demazure, Désingularisation des variétés de Schubert généralisées, Ann. Sci. El. Norm. Sup. 7 (1974), 53-88. | EuDML | Numdam | MR | Zbl

[10] H. Esnault, B. Kahn, M. Levine and E. Viehweg, The Arason invariant and mod 2 algebraic cycles, JAMS 11 (1998), no. 1, 73-118. | MR | Zbl

[11] H. Garland, The arithmetic theory of loop groups, Publ. Math. IHES 52 (1980), 181-312. | EuDML | Numdam | MR | Zbl

[12] J. Giraud, Méthode de la descente, Bull. SMF, mémoire, n°2 (1964). | EuDML | Numdam | MR | Zbl

[13] R. GODEMENT, Théorie des faisceaux, Hermann, Paris (1958). | MR

[14] A. Grothendieck, Sur quelques points d'algèbre homologique, Tôhoku Math. J. 9 (1957), 119-221. | Zbl

[15] B. Kahn, Descente galoisienne et K2 des corps de nombres, K-theory 7 (1) (1993). | MR | Zbl

[16] B. Kahn, Applications of weight two motivic cohomology, Doc. Math., (J. DMV) 1 (1996), 395-416. | EuDML | MR | Zbl

[17] M. Levine, The algebraic K-theory of the classical groups and some twisted forms, Duke Math. J. 70 (1993), 405-443. | MR | Zbl

[18] S. Lichtenbaum, The construction of weight two arithmetic cohomology, Inv. Math. 88 (1987), 183-215. | EuDML | MR | Zbl

[19] G. W. Mackey, Les ensembles boréliens et les extensions de groupes, J. Math. Pure et Appl. 36 (1957), 171-178. | MR | Zbl

[20] H. Matsumoto, Sur les sous-groupes arithmétiques des groupes semi-simples déployés, Ann. Sci. Ec. Norm. Sup. 2 (1969), 1-62. | EuDML | Numdam | MR | Zbl

[21] A. S. Merkurjev and A. Suslin, K -cohomology of Severi-Brauer varieties and the norm residue homomorphism, Math. USSR. Izv. 21 2 (1983), 307-340. | Zbl

[22] J. Milnor, Introduction to Algebraic K-Theory, Annals Math. Studies 72, Princeton University Press (1971). | MR | Zbl

[23] C. Moore, Group extensions of p-adic and adelic linear groups, Publ. Math. IHES 35 (1968), 40-86. | EuDML | Numdam | MR | Zbl

[24] G. Prasad and A. S. Rapinchuk, Computation of the metaplectic kernel, Publ. Math. IHES 84 (1996), 91-187. | EuDML | Numdam | MR | Zbl

[25] D. Quillen, Higher Algebraic K-Theory I, Batelle Institute Conference 1972, Lecture Notes in Math. 341 (1973), 85-147. | MR | Zbl

[26] G. Segal, The definition of conformal field theory, in: Differential geometric methods in mathematical physics (Como, 1987) 165-171, NATO Adv. Sci. Inst. Ser. C, Math. Phys. Sci. 250 (1988), Kluwer. | MR | Zbl

[27] C. C. Sherman, K-cohomology of coherent sheaves, Comm. Alg. 7 (1979), 990-1027. | MR | Zbl

[28] R. Steinberg, Générateurs, relations et revêtements de groupes algébriques (1962), Colloque sur la théorie des groupes algébriques, Bruxelles, 113-127. | MR | Zbl

[29] C. Soulé, K-théorie des anneaux d'entiers de corps de nombres et cohomologie étale, Inv. Math. 55 (1979), 251-295. | EuDML | Zbl

[30] A. A. Suslin, Torsion in K2 of fields, K-Theory 1 (1987), 5-29. | MR | Zbl

[31] J. Tate, Relations between K2 and Galois cohomology, Inv. Math. 36 (1976), 257-274. | EuDML | MR | Zbl

[32] J. Tits, Sur les constantes de structure et le théorème d'existence des algèbres de Lie semi-simples, Publ. Math. IHES 31 (1966), 21-58. | EuDML | Numdam | Zbl