Poincaré duality for Ext–groups between strict polynomial functors

Chałupnik, Marcin

doi:10.1090/proc12782

Poincaré duality for Ext–groups between strict polynomial functors
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by Marcin Chałupnik PDF

Proc. Amer. Math. Soc. 144 (2016), 963-970 Request permission

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.

References

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, DOI 10.1016/j.ansens.2005.07.002
Marcin Chałupnik, Koszul duality and extensions of exponential functors, Adv. Math. 218 (2008), no. 3, 969–982. MR 2414328, DOI 10.1016/j.aim.2008.02.008
Marcin Chałupnik, Extensions of Weyl and Schur functors, Homology Homotopy Appl. 11 (2009), no. 2, 27–48. MR 2529231, DOI 10.4310/HHA.2009.v11.n2.a3
M. Chałupnik, Derived Kan extension for strict polynomial functors, to appear in Int. Math. Research Notices.
Vincent Franjou and Eric M. Friedlander, Cohomology of bifunctors, Proc. Lond. Math. Soc. (3) 97 (2008), no. 2, 514–544. MR 2439671, DOI 10.1112/plms/pdn005
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, DOI 10.2307/121092
Eric M. Friedlander and Andrei Suslin, Cohomology of finite group schemes over a field, Invent. Math. 127 (1997), no. 2, 209–270. MR 1427618, DOI 10.1007/s002220050119
Robin Hartshorne, Residues and duality, Lecture Notes in Mathematics, No. 20, Springer-Verlag, Berlin-New York, 1966. Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64; With an appendix by P. Deligne. MR 0222093, DOI 10.1007/BFb0080482
Stuart Martin, Schur algebras and representation theory, Cambridge Tracts in Mathematics, vol. 112, Cambridge University Press, Cambridge, 1993. MR 1268640, DOI 10.1017/CBO9780511470899
Burt Totaro, Projective resolutions of representations of $\textrm {GL}(n)$, J. Reine Angew. Math. 482 (1997), 1–13. MR 1427655, DOI 10.1515/crll.1997.482.1
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, DOI 10.5802/aif.2133