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1997 | 153 | 1 | 59-80
Tytuł artykułu

Thick subcategories of the stable module category

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EN
Abstrakty
EN
We study the thick subcategories of the stable category of finitely generated modules for the principal block of the group algebra of a finite group G over a field of characteristic p. In case G is a p-group we obtain a complete classification of the thick subcategories. The same classification works whenever the nucleus of the cohomology variety is zero. In case the nucleus is nonzero, we describe some examples which lead us to believe that there are always infinitely many thick subcategories concentrated on each nonzero closed homogeneous subvariety of the nucleus.
Słowa kluczowe
Rocznik
Tom
153
Numer
1
Strony
59-80
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-10-11
poprawiono
1996-12-16
Twórcy
autor
Bibliografia
  • [1] D. J. Benson, Representations and Cohomology I, Cambridge Stud. Adv. Math. 30, Cambridge Univ. Press, 1990.
  • [2] D. J. Benson, Representations and Cohomology II, Cambridge Stud. Adv. Math. 31, Cambridge Univ. Press, 1991.
  • [3] D. J. Benson, Cohomology of modules in the principal block of a finite group, New York J. Math. 1 (1995), 196-205.
  • [4] D. J. Benson, J. F. Carlson and J. Rickard, Complexity and varieties for infinitely generated modules, Math. Proc. Cambridge Philos. Soc. 118 (1995), 223-243.
  • [5] D. J. Benson, J. F. Carlson and J. Rickard, Complexity and varieties for infinitely generated modules, II, Math. Proc. Cambridge Philos. Soc. to appear.
  • [6] D. J. Benson, J. F. Carlson and G. R. Robinson, On the vanishing of group cohomology, J. Algebra 131 (1990), 40-73.
  • [7] L. Chouinard, Projectivity and relative projectivity over group rings, J. Pure Appl. Algebra 7 (1976), 278-302.
  • [8] E. S. Devinatz, M. J. Hopkins and J. H. Smith, Nilpotence and stable homotopy theory, I, Ann. of Math. (2) 128 (1988), 207-241.
  • [9] K. Erdmann, Algebras and semidihedral defect groups I, Proc. London Math. Soc. 57 (1988), 109-150.
  • [10] K. Erdmann, Algebras and semidihedral defect groups II, Proc. London Math. Soc. 60 (1990), 123-165.
  • [11] M. J. Hopkins, Global methods in homotopy theory, in: Homotopy Theory (Durham, 1985), London Math. Soc. Lecture Note Ser. 117, Cambridge Univ. Press, 1987, 73-96.
  • [12] A. Neeman, Stable homotopy as a triangulated functor, Invent. Math. 109 (1992), 17-40.
  • [13] A. Neeman, The chromatic tower for D(R), Topology 31 (1992), 519-532.
  • [14] J. Rickard, Morita theory for derived categories, J. London Math. Soc. (2) 39 (1989), 436-456.
  • [15] J. Rickard, Derived categories and stable equivalence, J. Pure Appl. Algebra 61 (1989), 303-317.
  • [16] J. Rickard, Derived equivalences as derived functors, J. London Math. Soc. (2) 43 (1991), 37-48.
  • [17] J. Rickard, Splendid equivalences: derived categories and permutation modules, Proc. London Math. Soc. (3) 72 (1996), 331-358.
  • [18] J. Rickard, Idempotent modules in the stable category, J. London Math. Soc., to appear.
  • [19] G. Schneider, Die 2-modularen Darstellungen der Mathieu-Gruppe $M_{12}$, doctoral dissertation, Essen, 1981.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-fmv153i1p59bwm
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