Central extensions of reductive groups by
Jean-Luc Brylinski; Pierre Deligne
Publications Mathématiques de l'IHÉS (2001)
- Volume: 94, page 5-85
- ISSN: 0073-8301
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topBrylinski, Jean-Luc, and Deligne, Pierre. "Central extensions of reductive groups by $K_2$." Publications Mathématiques de l'IHÉS 94 (2001): 5-85. <http://eudml.org/doc/104179>.
@article{Brylinski2001,
author = {Brylinski, Jean-Luc, Deligne, Pierre},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {reductive groups; ; universal central extensions; simply connected algebraic groups},
language = {eng},
pages = {5-85},
publisher = {Institut des Hautes Etudes Scientifiques},
title = {Central extensions of reductive groups by $K_2$},
url = {http://eudml.org/doc/104179},
volume = {94},
year = {2001},
}
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
PB - Institut des Hautes Etudes Scientifiques
VL - 94
SP - 5
EP - 85
LA - eng
KW - reductive groups; ; universal central extensions; simply connected algebraic groups
UR - http://eudml.org/doc/104179
ER -
References
top- [1] S. BLOCH, Some formulas pertaining to the K-theory of commutative group schemes, J. Alg. 53 (1978), 304-326. Zbl0432.14014MR502630
- [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. Zbl0598.13007
- [3] S. BLOCH and K. KATO, p-adic étale cohomology, Publ. Math. IHES 63 (1986), 107-152. Zbl0613.14017MR849653
- [4] S. BLOCH and A. OGUS, Gersten’s conjecture and the homology of schemes, Ann. Sci. Ec. Norm. Sup. 7 (1974), 181-202. Zbl0307.14008
- [5] F. BRUHAT et J. TITS, Groupes réductifs sur un corps local II, Publ. Math. IHES 60 (1984), 5-184. Zbl0597.14041MR327923
- [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. Zbl0844.57025MR1291698
- [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. Zbl0527.14011MR688259
- [8] P. DELIGNE, Extensions centrales de groupes algébriques simplement connexes et cohomologie galoisienne, Publ. Math. IHES 84 (1996), 35-89. Zbl0930.20043MR1441006
- [9] M. DEMAZURE, Désingularisation des variétés de Schubert généralisées, Ann. Sci. El. Norm. Sup. 7 (1974), 53-88. Zbl0312.14009MR354697
- [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. Zbl1025.11009MR1460391
- [11] H. GARLAND, The arithmetic theory of loop groups, Publ. Math. IHES 52 (1980), 181-312. Zbl0475.17004MR601519
- [12] J. GIRAUD, Méthode de la descente, Bull. SMF, mémoire, n°2 (1964). Zbl0211.32902MR190142
- [13] R. GODEMENT, Théorie des faisceaux, Hermann, Paris (1958). Zbl0080.16201MR102797
- [14] A. GROTHENDIECK, Sur quelques points d’algèbre homologique, Tôhoku Math. J. 9 (1957), 119-221. Zbl0118.26104
- [15] B. KAHN, Descente galoisienne et K2 des corps de nombres, K-theory 7 (1) (1993). Zbl0780.12007MR1220427
- [16] B. KAHN, Applications of weight two motivic cohomology, Doc. Math., (J. DMV) 1 (1996), 395-416. Zbl0883.19002MR1423901
- [17] M. LEVINE, The algebraic K-theory of the classical groups and some twisted forms, Duke Math. J. 70 (1993), 405-443. Zbl0798.11009MR1219818
- [18] S. LICHTENBAUM, The construction of weight two arithmetic cohomology, Inv. Math. 88 (1987), 183-215. Zbl0615.14004MR877012
- [19] G. W. MACKEY, Les ensembles boréliens et les extensions de groupes, J. Math. Pure et Appl. 36 (1957), 171-178. Zbl0080.02303MR89998
- [20] H. MATSUMOTO, Sur les sous-groupes arithmétiques des groupes semi-simples déployés, Ann. Sci. Ec. Norm. Sup. 2 (1969), 1-62. Zbl0261.20025MR240214
- [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. Zbl0525.18008
- [22] J. MILNOR, Introduction to Algebraic K-Theory, Annals Math. Studies 72, Princeton University Press (1971). Zbl0237.18005MR349811
- [23] C. MOORE, Group extensions of p-adic and adelic linear groups, Publ. Math. IHES 35 (1968), 40-86. Zbl0159.03203MR244258
- [24] G. PRASAD and A. S. RAPINCHUK, Computation of the metaplectic kernel, Publ. Math. IHES 84 (1996), 91-187. Zbl0941.22019MR1441007
- [25] D. QUILLEN, Higher Algebraic K-Theory I, Batelle Institute Conference 1972, Lecture Notes in Math. 341 (1973), 85-147. Zbl0292.18004MR338129
- [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. Zbl0657.53060MR981378
- [27] C. C. SHERMAN, K-cohomology of coherent sheaves, Comm. Alg. 7 (1979), 990-1027. Zbl0425.18010MR541048
- [28] R. STEINBERG, Générateurs, relations et revêtements de groupes algébriques (1962), Colloque sur la théorie des groupes algébriques, Bruxelles, 113-127. Zbl0272.20036MR153677
- [29] C. SOULÉ, K-théorie des anneaux d’entiers de corps de nombres et cohomologie étale, Inv. Math. 55 (1979), 251-295. Zbl0437.12008
- [30] A. A. SUSLIN, Torsion in K2 of fields, K-Theory 1 (1987), 5-29. Zbl0635.12015MR899915
- [31] J. TATE, Relations between K2 and Galois cohomology, Inv. Math. 36 (1976), 257-274. Zbl0359.12011MR429837
- [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. Zbl0145.25804
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