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Transfers of Chern classes in BP-cohomology and Chow rings
Authors:
Björn Schuster and Nobuaki Yagita
Journal:
Trans. Amer. Math. Soc. 353 (2001), 1039-1054
MSC (2000):
Primary 55P35, 57T25; Secondary 55R35, 57T05
Posted:
August 8, 2000
MathSciNet review:
1804412
Full-text PDF Free Access
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Additional Information
Abstract: The  -module structure of  for extraspecial  -groups is studied using transfer and Chern classes. These give rise to  -torsion elements in the kernel of the cycle map from the Chow ring to ordinary cohomology first obtained by Totaro.
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(93b:20087), http://dx.doi.org/10.1112/blms/24.3.209
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John Green and Pham
Anh Minh, Transfer and Chern classes for extraspecial
𝑝-groups, Group representations: cohomology, group actions and
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Harada and Akira
Kono, On the integral cohomology of extraspecial 2-groups,
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(88b:20084), http://dx.doi.org/10.1016/0022-4049(87)90025-9
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C. Ravenel, Morava 𝐾-theories of classifying spaces and
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(93k:55008), http://dx.doi.org/10.1007/BFb0087510
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Kono and Nobuaki
Yagita, Brown-Peterson and ordinary cohomology
theories of classifying spaces for compact Lie groups, Trans. Amer. Math. Soc. 339 (1993), no. 2, 781–798. MR 1139493
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194 (1971), 197–212. MR 0290401
(44 #7582)
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D. C. Ravenel, W. S. Wilson and N. Yagita.
Brown-Peterson cohomology from Morava  -theory.
 -Theory 15 (1998), 147-199. CMP 99:02
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Björn
Schuster, On the Morava 𝐾-theory of some finite
2-groups, Math. Proc. Cambridge Philos. Soc. 121
(1997), no. 1, 7–13. MR 1418356
(97i:55008), http://dx.doi.org/10.1017/S0305004196001156
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Burt
Totaro, Torsion algebraic cycles and complex
cobordism, J. Amer. Math. Soc.
10 (1997), no. 2,
467–493. MR 1423033
(98a:14012), http://dx.doi.org/10.1090/S0894-0347-97-00232-4
- [T2]
B. Totaro.
The Chow ring of classifying spaces.
To appear.
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Nobuaki
Yagita, Cohomology for groups of
𝑟𝑎𝑛𝑘_{𝑝}𝐺=2 and
Brown-Peterson cohomology, J. Math. Soc. Japan 45
(1993), no. 4, 627–644. MR 1239340
(94k:55008), http://dx.doi.org/10.2969/jmsj/04540627
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Nobuaki
Yagita, On relations between Brown-Peterson cohomology and the
ordinary mod 𝑝 cohomology theory, Kodai Math. J.
7 (1984), no. 2, 273–285. MR 744140
(85g:55007), http://dx.doi.org/10.2996/kmj/1138036912
- [A]
- J. F. Adams.
Lectures on exceptional Lie groups,
edited by Z. Mahmud and M. Mimura.
Chicago Lectures in Mathematics, The University of Chicago Press, 1996. MR 98b:22001
- [BC]
- D. J. Benson and J. F. Carlson.
The cohomology of extraspecial groups.
Bull. London Math. Soc. 24 (1992), 209-235; erratum 25 (1993), 498. MR 93b:20087; MR 94f:20099
- [GL]
- D. J. Green and I. J. Leary.
The spectrum of the Chern subring.
Comm. Math. Helv. 73 (1998), 406-426. MR 99j:20070
- [GM]
- D. Green and P. A. Minh.
Transfer and Chern classes for extraspecial  -groups.
In: A. Adem, J. F. Carlson, S. B. Priddy and P. J. Webb, Eds.
Group representations: cohomology, group actions and topology (Seattle, WA, 1996).
Proc. Sympos. Pure Math. 63, pp. 245-255, Amer. Math. Soc., Providence, RI, 1998. MR 99d:20083
- [HK]
- M. Harada and A. Kono.
On the integral cohomology of extraspecial  -groups.
Proceedings of the Northwestern conference on cohomology of groups (Evanston, Ill., 1985).
J. Pure Appl. Algebra 44 (1987), 215-219. MR 88b:20084
- [HKR]
- M. J. Hopkins, N. J. Kuhn, and D. C. Ravenel.
Morava  -theories of classifying spaces and generalized characters for finite groups.
In: J. Aguadé, M. Castellet and F. R. Cohen, Eds.
Algebraic topology (Sant Feliu de Guíxols, 1990).
Lecture Notes in Math. 1509 (1992), Springer, 186-209. MR 93k:55008
- [KY]
- A. Kono and N. Yagita.
Brown-Peterson and ordinary cohomology theories of classifying spaces for compact Lie groups.
Trans. Amer. Math. Soc. 339 (1993), 781-798. MR 93m:55006
- [K]
- I. Kriz.
Morava  -theory of classifying spaces: some calculations.
Topology 36 (1997), 1247-1273. MR 99a:55016
- [Q]
- D. G. Quillen.
The mod  cohomology rings of extra-special 2-groups and the spinor groups.
Math. Ann. 194 (1971), 197-212. MR 44:7582
- [RWY]
- D. C. Ravenel, W. S. Wilson and N. Yagita.
Brown-Peterson cohomology from Morava -theory.
-Theory 15 (1998), 147-199. CMP 99:02
- [S]
- B. Schuster.
On the Morava  -theory of some finite  -groups.
Math. Proc. Cambridge Philos. Soc. 121 (1997), 7-13. MR 97i:55008
- [T1]
- B. Totaro.
Torsion algebraic cycles and complex cobordism.
J. Amer. Math. Soc. 10 (1997), 467-493. MR 98a:14012
- [T2]
- B. Totaro.
The Chow ring of classifying spaces.
To appear.
- [Y1]
- N. Yagita.
Cohomology for groups of rank and Brown-Peterson cohomology.
J. Math. Soc. Japan 45 (1993), 627-644. MR 94k:55008
- [Y2]
- N. Yagita.
On relations between Brown-Peterson cohomology and the ordinary mod  cohomology theory.
Kodai Math.J 7 (1984), 273-285. MR 85g:55007
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Additional Information
Björn Schuster
Affiliation:
FB 7 Mathematik, Bergische Universität-Gesamthochschule Wuppertal, 42097 Wuppertal, Germany
Email:
schuster@math.uni-wuppertal.de
Nobuaki Yagita
Affiliation:
Department of Mathematics, Faculty of Education, Ibaraki University, Mito, Ibaraki, Japan
Email:
yagita@mito.ipc.ibaraki.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002-9947-00-02647-7
PII:
S 0002-9947(00)02647-7
Keywords:
BP-theory,
transfer,
Chern classes,
Chow ring
Received by editor(s):
March 29, 1999
Posted:
August 8, 2000
Article copyright:
© Copyright 2000 American Mathematical Society
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