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Poincaré duality for Ext-groups between strict polynomial functors

Author: Marcin Chałupnik
Journal: Proc. Amer. Math. Soc. 144 (2016), 963-970
MSC (2010): Primary 18A25, 18A40, 18G15, 20G15
Published electronically: July 1, 2015
MathSciNet review: 3447650
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Abstract: We study the relation between left and right adjoint functors to the precomposition functor. As a consequence, we obtain various dualities for the Ext-groups in the category of strict polynomial functors.

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  • [C1] Marcin Chałupnik, Extensions of strict polynomial functors, Ann. Sci. École Norm. Sup. (4) 38 (2005), no. 5, 773-792 (English, with English and French summaries). MR 2195259 (2006k:20090),
  • [C2] Marcin Chałupnik, Koszul duality and extensions of exponential functors, Adv. Math. 218 (2008), no. 3, 969-982. MR 2414328 (2009i:18012),
  • [C3] Marcin Chałupnik, Extensions of Weyl and Schur functors, Homology, Homotopy Appl. 11 (2009), no. 2, 27-48. MR 2529231 (2010f:18009)
  • [C4] M. Chałupnik, Derived Kan extension for strict polynomial functors, to appear in Int. Math. Research Notices.
  • [FF] Vincent Franjou and Eric M. Friedlander, Cohomology of bifunctors, Proc. Lond. Math. Soc. (3) 97 (2008), no. 2, 514-544. MR 2439671 (2009m:20075),
  • [FFSS] Vincent Franjou, Eric M. Friedlander, Alexander Scorichenko, and Andrei Suslin, General linear and functor cohomology over finite fields, Ann. of Math. (2) 150 (1999), no. 2, 663-728. MR 1726705 (2001b:14076),
  • [FS] Eric M. Friedlander and Andrei Suslin, Cohomology of finite group schemes over a field, Invent. Math. 127 (1997), no. 2, 209-270. MR 1427618 (98h:14055a),
  • [Ha] Robin Hartshorne, Residues and duality, Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64. With an appendix by P. Deligne. Lecture Notes in Mathematics, No. 20, Springer-Verlag, Berlin-New York, 1966. MR 0222093 (36 #5145)
  • [Ma] Stuart Martin, Schur algebras and representation theory, Cambridge Tracts in Mathematics, vol. 112, Cambridge University Press, Cambridge, 1993. MR 1268640 (95f:20071)
  • [To] Burt Totaro, Projective resolutions of representations of $ {\rm GL}(n)$, J. Reine Angew. Math. 482 (1997), 1-13. MR 1427655 (98h:20080),
  • [Tr] Alain Troesch, Une résolution injective des puissances symétriques tordues, Ann. Inst. Fourier (Grenoble) 55 (2005), no. 5, 1587-1634 (French, with English and French summaries). MR 2172274 (2006g:18011)

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Additional Information

Marcin Chałupnik
Affiliation: Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02–097 Warsaw, Poland

Keywords: Strict polynomial functor, Poincar\'e duality, Ext--group
Received by editor(s): November 13, 2014
Received by editor(s) in revised form: March 3, 2015
Published electronically: July 1, 2015
Additional Notes: The author was supported by the grant (NCN) 2011/01/B/ST1/06184
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2015 American Mathematical Society

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