Duals and admissibility in natural characteristic

Schneider, Peter; Sorensen, Claus

doi:10.1090/ert/634

Duals and admissibility in natural characteristic
HTML articles powered by AMS MathViewer

by Peter Schneider and Claus Sorensen;

Represent. Theory 27 (2023), 30-50

DOI: https://doi.org/10.1090/ert/634

Published electronically: March 15, 2023

HTML | PDF | Request permission

Abstract:

In this article we introduce a derived smooth duality functor $R\underline {Hom}(-,k)$ on the unbounded derived category $D(G)$ of smooth $k$-representations of a $p$-adic Lie group $G$. Here $k$ is a field of characteristic $p$. Using this functor we relate various subcategories of admissible complexes in $D(G)$.

References

Armand Brumer, Pseudocompact algebras, profinite groups and class formations, J. Algebra 4 (1966), 442–470. MR 202790, DOI 10.1016/0021-8693(66)90034-2
Matthew Emerton, Ordinary parts of admissible representations of $p$-adic reductive groups I. Definition and first properties, Astérisque 331 (2010), 355–402 (English, with English and French summaries). MR 2667882
Matthew Emerton, Ordinary parts of admissible representations of $p$-adic reductive groups II. Derived functors, Astérisque 331 (2010), 403–459 (English, with English and French summaries). MR 2667883
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 222093, DOI 10.1007/BFb0080482
Masaki Kashiwara and Pierre Schapira, Categories and sheaves, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 332, Springer-Verlag, Berlin, 2006. MR 2182076, DOI 10.1007/3-540-27950-4
Jan Kohlhaase, Smooth duality in natural characteristic, Adv. Math. 317 (2017), 1–49. MR 3682662, DOI 10.1016/j.aim.2017.06.038
Karol Kozioł, Hecke module structure on first and top pro-$p$-Iwahori cohomology, Acta Arith. 186 (2018), no. 4, 349–376. MR 3879398, DOI 10.4064/aa170903-24-3
Karol Kozioł, Functorial properties of pro-$p$-Iwahori cohomology, J. Lond. Math. Soc. (2) 104 (2021), no. 4, 1572–1614. MR 4339945, DOI 10.1112/jlms.12469
K. Koziol and D. Schwein, On mod p orientation characters, Preprint, http://www-personal.umich.edu/~kkoziol/orientation.pdf, 2021.
Joseph Oesterlé, Nombres de Tamagawa et groupes unipotents en caractéristique $p$, Invent. Math. 78 (1984), no. 1, 13–88 (French). MR 762353, DOI 10.1007/BF01388714
Rachel Ollivier and Peter Schneider, The modular pro-$p$ Iwahori-Hecke Ext-algebra, Representations of reductive groups, Proc. Sympos. Pure Math., vol. 101, Amer. Math. Soc., Providence, RI, 2019, pp. 255–308. MR 3930021, DOI 10.1090/pspum/101/11
Peter Schneider, $p$-adic Lie groups, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 344, Springer, Heidelberg, 2011. MR 2810332, DOI 10.1007/978-3-642-21147-8
Peter Schneider, Smooth representations and Hecke modules in characteristic $p$, Pacific J. Math. 279 (2015), no. 1-2, 447–464. MR 3437786, DOI 10.2140/pjm.2015.279.447
Jean-Pierre Serre, Cohomologie galoisienne, Lecture Notes in Mathematics, No. 5, Springer-Verlag, Berlin-New York, 1965 (French). With a contribution by Jean-Louis Verdier; Troisième édition, 1965. MR 201444, DOI 10.1007/978-3-662-21576-0
Charles A. Weibel, An introduction to homological algebra, Cambridge Studies in Advanced Mathematics, vol. 38, Cambridge University Press, Cambridge, 1994. MR 1269324, DOI 10.1017/CBO9781139644136

AMS Website Down

Representation Theory

Duals and admissibility in natural characteristic
HTML articles powered by AMS MathViewer

Abstract: