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2014 | 12 | 2 | 212-228
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Stable cohomology of alternating groups

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We determine the stable cohomology groups ($$H_S^i \left( {{{\mathfrak{A}_n ,\mathbb{Z}} \mathord{\left/ {\vphantom {{\mathfrak{A}_n ,\mathbb{Z}} {p\mathbb{Z}}}} \right. \kern-\nulldelimiterspace} {p\mathbb{Z}}}} \right)$$ of the alternating groups $$\mathfrak{A}_n$$ for all integers n and i, and all odd primes p.
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
2
Strony
212-228
Opis fizyczny
Daty
wydano
2014-02-01
online
2013-11-21
Twórcy
Bibliografia
  • [1] Adem A., Milgram R.J., Cohomology of Finite Groups, 2nd ed., Grundlehren Math. Wiss., 309, Springer, Berlin, 2004 http://dx.doi.org/10.1007/978-3-662-06280-7
  • [2] 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
  • [3] Bogomolov F., Stable cohomology of finite and profinite groups, In: Algebraic Groups, Göttingen, June 27–July 13, 2005, Universitätsverlag Göttingen, Göttingen, 2007, 19–49
  • [4] Bogomolov F., Böhning Chr., Isoclinism and stable cohomology of wreath products, In: Birational Geometry, Rational Curves, and Arithmetic, Simons Symposium ”Geometry Over Non-Closed Fields”, St. John, February 26–March 3, 2012, Springer, New York, 2013, 57–76
  • [5] Bogomolov F., Petrov T., Unramified cohomology of alternating groups, Cent. Eur. J. Math., 2011, 9(5), 936–948 http://dx.doi.org/10.2478/s11533-011-0061-8
  • [6] 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
  • [7] 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
  • [8] Colliot-Thélène J.-L., Ojanguren M., Variétés unirationelles non rationelles: au-delà de l’exemple d’Artin et Mumford, Invent. Math., 1989, 97(1), 141–158 http://dx.doi.org/10.1007/BF01850658
  • [9] Garibaldi S., Merkurjev A., Serre J.-P., Cohomological invariants in Galois cohomology, Univ. Lecture Ser., 28, American Mathematical Society, Providence, 2003
  • [10] Kahn B., Relatively unramified elements in cycle modules, J. K-Theory, 2011, 7(3), 409–427 http://dx.doi.org/10.1017/is011003002jkt147
  • [11] Kahn B., Sujatha R., Motivic cohomology and unramified cohomology of quadrics, J. Eur. Math. Soc. (JEMS), 2000, 2(2), 145–177 http://dx.doi.org/10.1007/s100970000015
  • [12] 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
  • [13] Mùi H., Modular invariant theory and cohomology algebras of symmetric groups, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 1975, 22(3), 319–369
  • [14] Nguyen T.K.N., Modules de Cycles et Classes Non Ramifiées sur un Espace Classifiant, PhD thesis, Université Paris Diderot, 2010
  • [15] Nguyen T.K.N., Classes non ramifiées sur un espace classifiant, C. R. Math. Acad. Sci. Paris, 2011, 349(5–6), 233–237 http://dx.doi.org/10.1016/j.crma.2011.02.012
  • [16] Ore O., Theory of monomial groups, Trans. Amer. Math. Soc., 1942, 51(1), 15–64 http://dx.doi.org/10.2307/1989979
  • [17] Serre J.-P., Galois Cohomology, Springer Monogr. Math., Springer, Berlin, 2002
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  • [19] Tezuka M., Yagita N., The image of the map from group cohomology to Galois cohomology, Trans. Amer. Math. Soc., 2011, 363(8), 4475–4503 http://dx.doi.org/10.1090/S0002-9947-2011-05418-8
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0336-3
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