Chern subrings
HTML articles powered by AMS MathViewer
- by Masaki Kameko and Nobuaki Yagita PDF
- Proc. Amer. Math. Soc. 138 (2010), 367-373 Request permission
Abstract:
Let $p$ be an odd prime. We show that for a simply connected semisimple complex linear algebraic group, if its integral homology has $p$-torsion, the Chern classes do not generate the Chow ring of its classifying space.References
- J. F. Adams, Lectures on exceptional Lie groups, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1996. With a foreword by J. Peter May; Edited by Zafer Mahmud and Mamoru Mimura. MR 1428422
- K. K. S. Andersen, J. Grodal, J. M. Mรธller, and A. Viruel, The classification of $p$-compact groups for $p$ odd, Ann. of Math. (2) 167 (2008), no.ย 1, 95โ210. MR 2373153, DOI 10.4007/annals.2008.167.95
- Masaki Kameko and Mamoru Mimura, Mรนi invariants and Milnor operations, Proceedings of the School and Conference in Algebraic Topology, Geom. Topol. Monogr., vol. 11, Geom. Topol. Publ., Coventry, 2007, pp.ย 107โ140. MR 2402803
- Masaki Kameko and Nobuaki Yagita, The Brown-Peterson cohomology of the classifying spaces of the projective unitary groups $\textrm {PU}(p)$ and exceptional Lie groups, Trans. Amer. Math. Soc. 360 (2008), no.ย 5, 2265โ2284. MR 2373313, DOI 10.1090/S0002-9947-07-04425-X
- Akira Kono and Nobuaki Yagita, Brown-Peterson and ordinary cohomology theories of classifying spaces for compact Lie groups, Trans. Amer. Math. Soc. 339 (1993), no.ย 2, 781โ798. MR 1139493, DOI 10.1090/S0002-9947-1993-1139493-4
- Mamoru Mimura and Tetsu Nishimoto, On the Stiefel-Whitney classes of the representations associated with $\rm Spin(15)$, Proceedings of the School and Conference in Algebraic Topology, Geom. Topol. Monogr., vol. 11, Geom. Topol. Publ., Coventry, 2007, pp.ย 141โ176. MR 2402804
- Jean-Pierre Serre, Linear representations of finite groups, Graduate Texts in Mathematics, Vol. 42, Springer-Verlag, New York-Heidelberg, 1977. Translated from the second French edition by Leonard L. Scott. MR 0450380
- Bjรถrn Schuster and Nobuaki Yagita, Transfers of Chern classes in BP-cohomology and Chow rings, Trans. Amer. Math. Soc. 353 (2001), no.ย 3, 1039โ1054. MR 1804412, DOI 10.1090/S0002-9947-00-02647-7
- Elisa Targa, Chern classes are not enough. Appendix to: โOn the cohomology and the Chow ring of the classifying space of $\textrm {PGL}_p$โ [J. Reine Angew. Math. 610 (2007), 181โ227; MR2359886] by A. Vistoli, J. Reine Angew. Math. 610 (2007), 229โ233. MR 2359887, DOI 10.1515/CRELLE.2007.072
- Burt Totaro, The Chow ring of a classifying space, Algebraic $K$-theory (Seattle, WA, 1997) Proc. Sympos. Pure Math., vol. 67, Amer. Math. Soc., Providence, RI, 1999, pp.ย 249โ281. MR 1743244, DOI 10.1090/pspum/067/1743244
- Angelo Vistoli, On the cohomology and the Chow ring of the classifying space of $\textrm {PGL}_p$, J. Reine Angew. Math. 610 (2007), 181โ227. MR 2359886, DOI 10.1515/CRELLE.2007.071
- Vladimir Voevodsky, Reduced power operations in motivic cohomology, Publ. Math. Inst. Hautes รtudes Sci. 98 (2003), 1โ57. MR 2031198, DOI 10.1007/s10240-003-0009-z
- Nobuaki Yagita, Applications of Atiyah-Hirzebruch spectral sequences for motivic cobordism, Proc. London Math. Soc. (3) 90 (2005), no.ย 3, 783โ816. MR 2137831, DOI 10.1112/S0024611504015084
Additional Information
- Masaki Kameko
- Affiliation: Faculty of Contemporary Society, Toyama University of International Studies, Toyama 930-1292, Japan
- Email: kameko@tuins.ac.jp
- Nobuaki Yagita
- Affiliation: Faculty of Education, Ibaraki University, Mito, Ibaraki, Japan
- MR Author ID: 185110
- Email: yagita@mx.ibaraki.ac.jp
- Received by editor(s): November 2, 2008
- Received by editor(s) in revised form: May 7, 2009
- Published electronically: August 20, 2009
- Additional Notes: The authors are partially supported by the Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C) 19540105, 20540061, respectively.
- Communicated by: Paul Goerss
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 367-373
- MSC (2000): Primary 55R40, 57T15, 20J06, 20J05
- DOI: https://doi.org/10.1090/S0002-9939-09-10042-4
- MathSciNet review: 2550202