Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-30T00:11:14.641Z Has data issue: false hasContentIssue false
  • English
  • Français

Coniveau spectral sequences of classifying spaces for exceptional and Spin groups

Published online by Cambridge University Press:  22 September 2011

M. KAMEKO ,
M. TEZUKA  and
N. YAGITA
M. KAMEKO
Affiliation:
Department of Mathematical Sciences, College of Systems Engineering and Science, Shibaura Institute of Technology, Saitama, Japan. e-mail: [email protected]
M. TEZUKA
Affiliation:
Department of mathematics, Faculty of Science, Ryukyu University, Okinawa, Japan. e-mail: [email protected]
N. YAGITA
Affiliation:
Faculty of Education, Ibaraki University, Mito, Ibaraki, Japan. e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Let k be an algebraically closed field of ch(k) = 0 and G be a simple simply connected algebraic group G over k. By using results about cohomological invariants, we compute the coniveau spectral sequence for classifying spaces BG.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 152 , Issue 2 , March 2012 , pp. 251 - 278
Copyright
Copyright © Cambridge Philosophical Society 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Adams, J. F.Lectures on exceptional Lie groups (University Chicago Press, 1996).Google Scholar
[2]Bloch, S. and Ogus, A.Gersten's conjecture and the homology of schemes. Ann. Sci. École. Norm. Sup. 7 (1974), 181–202.CrossRefGoogle Scholar
[3]Garibaldi, S.Cohomological invariants: exceptional groups and Spin groups (wth an appendix by D. Hoffmann). Mem. Amer. Math. Soc. 200 (2009).Google Scholar
[4]Garibaldi, S., Merkurjev, A. and Serre, J. P. Cohomological invariants in Galois cohomology. University lecture. series vol (28) Amer. Math. Soc. (2003).CrossRefGoogle Scholar
[5]Guillot, P.The Chow ring of G 2 and Spin (7). J. Reine Angew. Math. 604 (2007), 137–158.Google Scholar
[6]Hazewinkel, M. Formal groups and applications. Pure Appl. Math. (1978), xxii+573pp.Google Scholar
[7]Kameko, M. and Mimura, M.Mùi invariants and Milnor operations, Geom. Topol. Monogr. 11 (2007), 107–140.Google Scholar
[8]Kameko, M. and Yagita, N.The Brown–Peterson cohomology of the classifying spaces of the projective unitary groups PU(p) and exceptional Lie group. Trans. Amer. Math. Soc. 360 (2008), 2265–2284.CrossRefGoogle Scholar
[9]Kameko, M. and Yagita, N.Chern subrings. Proc. Amer. Math. Soc. 138 (2010), 367–373.CrossRefGoogle Scholar
[10]Kono, A. and Yagita, N.Brown–Peterson and ordinary cohomology theories of classifying spaces for compact Lie groups. Trans. Amer. Math. Soc. 339 (1993), no. 2, 781–798.CrossRefGoogle Scholar
[11]Kono, A. and Mimura, M.On cohomology mod 2 of the classifying space of compact Lie group type E 6. J. Pure Appl. Algebra 6 (1975), 61–81.CrossRefGoogle Scholar
[12]Molina, L. A. The Chow ring of the classifying space of Spin 8. Preprint (2007).CrossRefGoogle Scholar
[13]Molina, L. and Vistoli, A.On the Chow rings of classifying spaces for classical groups. Rend. Sem. Mat. Univ. Padova 116 (2006), 271–298.Google Scholar
[14]Mui, H.Modular invariant theory and cohomology algebras of symmetric groups. J. Fac. Soc. Tokyo Univ. 22 (1975), 319–369.Google Scholar
[15]Orlov, D., Vishik, A. and Voevodsky, V.An exact sequence for Milnor's K-theory with applications to quadratic forms. Ann. of Math. 165 (2007), 1–13.CrossRefGoogle Scholar
[16]Paranjape, W.Some spectral sequences for filtered complexes and applications. J. Algebra 186 (1996), 793–806.CrossRefGoogle Scholar
[17]Quillen, D.The spectrum of an equivarent cohomology ring I, II. Ann. of Math. 194 (1971), 549–572, 573–602.CrossRefGoogle Scholar
[18]Rost, M. On the basic correspondence of a splitting variety. Preprint (2006)Google Scholar
[19]Schuster, B. and Yagita, N.Transfers of Chern classes in BP-cohomology and Chow rings. Trans. Amer. Math. Soc. 353 (2001), no. 3, 1039–1054.CrossRefGoogle Scholar
[20]Suslin, A. and Joukhovistski, S.Norm Varieties. J. Pure Appl. Alg. 206 (2006), 245–276.CrossRefGoogle Scholar
[21]Totaro, B.The Chow ring of classifying spaces. Proc. of Symposia in Pure Math. “Algebraic K-theory” (1997: University of Washington, Seattle) 67 (1999), 248–281.Google Scholar
[22]Voevodsky, V. The Milnor conjecture. www.math.uiuc.edu/K-theory/0170 (1996).Google Scholar
[23]Voevodsky, V.Motivic cohomology with ℤ/2 coefficient. Publ. Math. Inst. Hautes. Études. Sci. 98 (2003), 59–104.CrossRefGoogle Scholar
[24]Voevodsky, V. (Notes by C. Weibel). Voevodsky's Seattle lectures: K-theory and motivic cohomology Proc. of Symposia in Pure Math. “Algebraic K-theory” (1997: University of Washington, Seattle) 67 (1999), 283–303.CrossRefGoogle Scholar
[25]Voevodsky, V.Reduced power operations in motivic cohomology. Publ. Math. Inst. Hautes. Études. Sci. 98 (2003), 1–57.CrossRefGoogle Scholar
[26]Voevodsky, V. On motivic cohomology with ℤ/l-coefficients. www.math.uiuc.edu/K-theory/0631 (2003).Google Scholar
[27]Yagita, N.Examples for the mod p motivic cohomology of classifying spaces. Trans. Amer. Math. Soc. 355 (2003), 4427–4450.CrossRefGoogle Scholar
[28]Yagita, N.Applications of Atiyah–Hirzebruch spectral sequence for motivic cobordism. Proc. London Math. Soc. 90 (2005), 783–816.CrossRefGoogle Scholar
[29]Yagita, N.Coniveau filtration of cohomology of groups. Proc. London Math. Soc. 101 (2010), 179–206.CrossRefGoogle Scholar