Ordinary parts of admissible representations of $p$-adic reductive groups I. Definition and first properties

Ordinary parts of admissible representations of

p

-adic reductive groups I. Definition and first properties

Emerton, Matthew

Représentations

p

-adiques de groupes

p

-adiques III : méthodes globales et géométriques, Astérisque, no. 331 (2010), pp. 355-402.

MR Zbl | 6 citations dans Numdam

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     author = {Emerton, Matthew},
     title = {Ordinary parts of admissible representations of $p$-adic reductive groups {I.} {Definition} and first properties},
     booktitle = {Repr\'esentations $p$-adiques de groupes $p$-adiques III : m\'ethodes globales et g\'eom\'etriques},
     series = {Ast\'erisque},
     pages = {355--402},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {331},
     year = {2010},
     mrnumber = {2667882},
     zbl = {1205.22013},
     language = {en},
     url = {https://numdam.org/item/AST_2010__331__355_0/}
}

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Emerton, Matthew. Ordinary parts of admissible representations of $p$-adic reductive groups I. Definition and first properties, dans Représentations $p$-adiques de groupes $p$-adiques III : méthodes globales et géométriques, Astérisque, no. 331 (2010), pp. 355-402. https://numdam.org/item/AST_2010__331__355_0/

Bibliographie
Cité par

[1] L. Barthel & R. Livné - "Irreducible modular representations of $G L_{2}$ of a local field", Duke Math. J. 75 (1994), p. 261-292. | DOI | MR | Zbl

[2] C. Breuil - "Sur quelques représentations modulaires et $p$ -adiques de $G L_{2} (𝐐_{p})$ . I", Compositio Math. 138 (2003), p. 165-188. | DOI | MR | Zbl

[3] W. Casselman - "Introduction to the theory of admissible representations of $p$ -adic reductive groups", unpublished notes distributed by P. Sally, draft May 1 1995, http://www.math.ubc.ca/~cass/research/pdf/p-adic-book.pdf.

[4] P. Colmez - "Représentations de $G L_{2} (𝐐_{p})$ et $(φ, Γ)$ -modules", Astérisque 330 (2010), p. 281-509. | Numdam | MR | Zbl

[5] M. Emerton - "Jacquet modules of locally analytic representations of $p$ -adic reductive groups. I. Construction and first properties", Ann. Sci. École Norm. Sup. 39 (2006), p. 775-839. | DOI | EuDML | Numdam | MR | Zbl

[6] M. Emerton - "On the interpolation of systems of eigenvalues attached to automorphic Hecke eigenforms", Invent Math. 164 (2006), p. 1-84. | DOI | MR | Zbl

[7] M. Emerton - "Jacquet modules of locally analytic representations of $p$ -adic reductive groups II. The relation to parabolic induction", preprint http://www.math.northwestern.edu/~emerton/pdffiles/jacquêt-two.pdf, 2007.

[8] M. Emerton - "Local-global compatibility in the $p$ -adic langlands programme for $G L_{2 / ℚ}$ ", in preparation. | MR

[9] M. Emerton - "Locally analytic vectors in representations of locally $p$ -adic analytic groups", to appear in Memoirs of the Amer. Math. Soc. | MR

[10] M. Emerton - "Ordinary parts of admissible representations of $p$ -adic reductive groups II. Derived functors", this volume. | Numdam | Zbl

[11] H. Hida - "Galois representations into $G L_{2} (𝐙_{p} [[X]])$ attached to ordinary cusp forms", Invent. Math. 85 (1986), p. 545-613. | DOI | EuDML | MR | Zbl

[12] H. Hida - " $p$ -ordinary cohomology groups for $S L (2)$ over number fields", Duke Math. J. 69 (1993), p. 259-314. | DOI | MR | Zbl

[13] H. Hida - "Control theorems of $p$ -nearly ordinary cohomology groups for $S L (n)$ ", Bull. Soc. Math. France 123 (1995), p. 425-475. | DOI | EuDML | Numdam | MR | Zbl

[14] M. Lazard - "Groupes analytiques $p$ -adiques", Publ. Math. I.H.É.S. 26 (1965), p. 5-219. | EuDML | Numdam

[15] P. Schneider & J. Teitelbaum - "Banach space representations and Iwasawa theory", Israel J. Math. 127 (2002), p. 359-380 | DOI | MR | Zbl