We extend the classical rigidity results for K-theory to the equivariant setting of linear algebraic group actions. These results concern rigidity for rational points, field extensions, and Hensel local rings.
Nous étendons les théorèmes de rigidité classiques pour la K-théorie au cadre équivariant de actions des groupes algébriques linéaire. Ces résultats concernent la rigidité pour les points rationels, les extensions de corps et les anneaux locaux henséliens.
Accepted:
Published online:
@article{CRMATH_2009__347_23-24_1403_0, author = {Yagunov, Serge and {\O}stv{\ae}r, Paul Arne}, title = {Rigidity for equivariant {\protect\emph{K}-theory}}, journal = {Comptes Rendus. Math\'ematique}, pages = {1403--1407}, publisher = {Elsevier}, volume = {347}, number = {23-24}, year = {2009}, doi = {10.1016/j.crma.2009.10.020}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2009.10.020/} }
TY - JOUR AU - Yagunov, Serge AU - Østvær, Paul Arne TI - Rigidity for equivariant K-theory JO - Comptes Rendus. Mathématique PY - 2009 SP - 1403 EP - 1407 VL - 347 IS - 23-24 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.10.020/ DO - 10.1016/j.crma.2009.10.020 LA - en ID - CRMATH_2009__347_23-24_1403_0 ER -
%0 Journal Article %A Yagunov, Serge %A Østvær, Paul Arne %T Rigidity for equivariant K-theory %J Comptes Rendus. Mathématique %D 2009 %P 1403-1407 %V 347 %N 23-24 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.10.020/ %R 10.1016/j.crma.2009.10.020 %G en %F CRMATH_2009__347_23-24_1403_0
Yagunov, Serge; Østvær, Paul Arne. Rigidity for equivariant K-theory. Comptes Rendus. Mathématique, Volume 347 (2009) no. 23-24, pp. 1403-1407. doi : 10.1016/j.crma.2009.10.020. http://www.numdam.org/articles/10.1016/j.crma.2009.10.020/
[1] The Bloch–Ogus–Gabber Theorem, Fields Institute Commun., vol. 16, Amer. Math. Soc., Providence, 1997, pp. 31-94
[2] K-theory of Henselian local rings and Henselian pairs, Santa Margherita Ligure, 1989 (Contemp. Math.), Volume vol. 126, Amer. Math. Soc., Providence, RI (1992), pp. 59-70
[3] H.A. Gillet, R.W. Thomason, The K-theory of strict Hensel local rings and a theorem of Suslin, in: Proceedings of the Luminy Conference on Algebraic K-Theory, Luminy, 1983, vol. 34, 1984, pp. 241–254
[4] Éléments de géométrie algébrique. III. Étude cohomologique des faisceaux cohérents. I, Inst. Hautes Études Sci. Publ. Math., Volume 11 (1961), p. 167
[5] Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, Springer-Verlag, New York, 1977
[6] Rigidity for Henselian local rings and -representable theories, Math. Z., Volume 255 (2007) no. 2, pp. 437-449
[7] Gersten conjecture for equivariant K-theory and applications, 2009 (preprint) | arXiv
[8] Étale Cohomology, Princeton Mathematical Series, vol. 33, Princeton Univ. Press, Princeton, NJ, 1980
[9] Rigidity for orientable functors, J. Pure Appl. Algebra, Volume 172 (2002) no. 1, pp. 49-77
[10] Higher algebraic K-theory. I, Battelle Memorial Inst., Seattle, Wash., 1972 (Lecture Notes in Math.), Volume vol. 341, Springer, Berlin (1973), pp. 85-147
[11] On the K-theory of algebraically closed fields, Invent. Math., Volume 73 (1983) no. 2, pp. 241-245
[12] A.A. Suslin, On the K-theory of local fields, in: Proceedings of the Luminy Conference on Algebraic K-Theory, Luminy, 1983, vol. 34, 1984, pp. 301–318
[13] Algebraic K-theory of fields, Berkeley, Calif., 1986, Amer. Math. Soc., Providence, RI (1987), pp. 222-244
[14] Algebraic K-theory of group scheme actions, Princeton, NJ, 1983 (Ann. of Math. Stud.), Volume vol. 113, Princeton Univ. Press, Princeton, NJ (1987), pp. 539-563
[15] Equivariant algebraic vs. topological K-homology Atiyah–Segal-style, Duke Math. J., Volume 56 (1988) no. 3, pp. 589-636
Cited by Sources: