Unramified cohomology of alternating groups

Fedor Bogomolov; Tihomir Petrov

Open Mathematics (2011)

  • Volume: 9, Issue: 5, page 936-948
  • ISSN: 2391-5455

Abstract

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We prove vanishing results for the unramified stable cohomology of alternating groups.

How to cite

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Fedor Bogomolov, and Tihomir Petrov. "Unramified cohomology of alternating groups." Open Mathematics 9.5 (2011): 936-948. <http://eudml.org/doc/269586>.

@article{FedorBogomolov2011,
abstract = {We prove vanishing results for the unramified stable cohomology of alternating groups.},
author = {Fedor Bogomolov, Tihomir Petrov},
journal = {Open Mathematics},
keywords = {Rationality; Alternating groups; Unramified cohomology; alternating groups; unramified cohomology; stable cohomology; rationality},
language = {eng},
number = {5},
pages = {936-948},
title = {Unramified cohomology of alternating groups},
url = {http://eudml.org/doc/269586},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Fedor Bogomolov
AU - Tihomir Petrov
TI - Unramified cohomology of alternating groups
JO - Open Mathematics
PY - 2011
VL - 9
IS - 5
SP - 936
EP - 948
AB - We prove vanishing results for the unramified stable cohomology of alternating groups.
LA - eng
KW - Rationality; Alternating groups; Unramified cohomology; alternating groups; unramified cohomology; stable cohomology; rationality
UR - http://eudml.org/doc/269586
ER -

References

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  1. [1] Adem A., Milgram R.J., Cohomology of Finite Groups, 2nd ed., Grundlehren Math. Wiss., 309, Springer, Berlin, 2004 Zbl1061.20044
  2. [2] Bogomolov F.A., The Brauer group of quotient spaces of linear representations, Math. USSR-Izv., 1988, 30(3), 455–485 http://dx.doi.org/10.1070/IM1988v030n03ABEH001024 Zbl0679.14025
  3. [3] Bogomolov F.A., Stable cohomology of groups and algebraic varieties, Russian Acad. Sci. Sb. Math., 1993, 76(1), 1–21 http://dx.doi.org/10.1070/SM1993v076n01ABEH003398 Zbl0789.14022
  4. [4] Bogomolov F., Maciel J., Petrov T., Unramified Brauer groups of finite simple groups of Lie type Al, Amer. J. Math., 2004, 126(4), 935–949 http://dx.doi.org/10.1353/ajm.2004.0024 Zbl1058.14031
  5. [5] Bogomolov F., Petrov T., Tschinkel Yu., Unramified cohomology of finite groups of Lie type, In: Cohomological and Geometric Approaches to Rationality Problems, Progr. Math., 282, Birkhäuser, Boston, 2010, 55–73 http://dx.doi.org/10.1007/978-0-8176-4934-0_3 
  6. [6] Colliot-Thélène J.-L., Birational invariants, purity and the Gersten conjecture, In: K-Theory and Algebraic Geometry: Connections with Quadratic Forms and Division Algebras, Santa Barbara, July 6–24, 1992, Proc. Sympos. Pure Math., 58(1), American Mathematical Society, Providence, 1995, 1–64 Zbl0834.14009
  7. [7] Colliot-Thélène J.-L., Ojanguren M., Variétés unirationnelles non rationnelles: au-delà de l’exemple d’Artin et Mumford, Invent. Math., 1989, 97(1), 141–158 http://dx.doi.org/10.1007/BF01850658 Zbl0686.14050
  8. [8] Fuks D.B., Cohomologies of the group COS mod 2, Funct. Anal. Appl., 1970, 4(2), 143–151 http://dx.doi.org/10.1007/BF01094491 Zbl0222.57031
  9. [9] Garibaldi S., Merkurjev A., Serre J.-P., Cohomological Invariants in Galois Cohomology, Univ. Lecture Ser., 28, American Mathematical Society, Providence, 2003 Zbl1159.12311
  10. [10] Kunyavskiĭ B., The Bogomolov multiplier of finite simple groups, In: Cohomological and Geometric Approaches to Rationality Problems, Progr. Math., 282, Birkhäuser, Boston, 2010, 209–217 http://dx.doi.org/10.1007/978-0-8176-4934-0_8 Zbl1204.14006
  11. [11] Mann B.M., The cohomology of the alternating groups, Michigan Math. J., 1985, 32(3), 267–277 http://dx.doi.org/10.1307/mmj/1029003238 Zbl0604.20053
  12. [12] Saltman D.J., Noether’s problem over an algebraically closed field, Invent. Math., 1984, 77(1), 71–84 http://dx.doi.org/10.1007/BF01389135 Zbl0546.14014
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