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Coniveau spectral sequences of classifying spaces for exceptional and Spin groups

Published online by Cambridge University Press:  22 September 2011

M. KAMEKO
Affiliation:
Department of Mathematical Sciences, College of Systems Engineering and Science, Shibaura Institute of Technology, Saitama, Japan. e-mail: kameko@shibaura-it.ac.jp
M. TEZUKA
Affiliation:
Department of mathematics, Faculty of Science, Ryukyu University, Okinawa, Japan. e-mail: tez@sci.u-ryukyu.ac.jp
N. YAGITA
Affiliation:
Faculty of Education, Ibaraki University, Mito, Ibaraki, Japan. e-mail: yagita@mx.ibaraki.ac.jp

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
Copyright
Copyright © Cambridge Philosophical Society 2011

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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), 181202.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), 137158.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), 107140.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), 22652284.CrossRefGoogle Scholar
[9]Kameko, M. and Yagita, N.Chern subrings. Proc. Amer. Math. Soc. 138 (2010), 367373.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, 781798.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), 6181.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), 271298.Google Scholar
[14]Mui, H.Modular invariant theory and cohomology algebras of symmetric groups. J. Fac. Soc. Tokyo Univ. 22 (1975), 319369.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), 113.CrossRefGoogle Scholar
[16]Paranjape, W.Some spectral sequences for filtered complexes and applications. J. Algebra 186 (1996), 793806.CrossRefGoogle Scholar
[17]Quillen, D.The spectrum of an equivarent cohomology ring I, II. Ann. of Math. 194 (1971), 549572, 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, 10391054.CrossRefGoogle Scholar
[20]Suslin, A. and Joukhovistski, S.Norm Varieties. J. Pure Appl. Alg. 206 (2006), 245276.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), 248281.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), 59104.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), 283303.CrossRefGoogle Scholar
[25]Voevodsky, V.Reduced power operations in motivic cohomology. Publ. Math. Inst. Hautes. Études. Sci. 98 (2003), 157.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), 44274450.CrossRefGoogle Scholar
[28]Yagita, N.Applications of Atiyah–Hirzebruch spectral sequence for motivic cobordism. Proc. London Math. Soc. 90 (2005), 783816.CrossRefGoogle Scholar
[29]Yagita, N.Coniveau filtration of cohomology of groups. Proc. London Math. Soc. 101 (2010), 179206.CrossRefGoogle Scholar