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Filtered modules with coefficients


Authors: Eknath Ghate and Ariane Mézard
Journal: Trans. Amer. Math. Soc. 361 (2009), 2243-2261
MSC (2000): Primary 11F80
DOI: https://doi.org/10.1090/S0002-9947-08-04829-0
Published electronically: December 15, 2008
MathSciNet review: 2471916
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Abstract: We classify the filtered modules with coefficients corresponding to two-dimensional potentially semi-stable $ p$-adic representations of the Galois group of $ \mathbf{Q}_p$ under some assumptions (e.g., $ p$ is odd). We focus on the new features that arise when the coefficients are not necessarily $ \mathbf{Q}_p$.


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  • [Ber04] L. Berger.
    An introduction to the theory of $ p$-adic representations,
    In Geometric aspects of Dwork theory,
    Vols. I, II, Walter de Gruyter GmbH & Co. KG, Berlin (2004), 255-292. MR 2023292 (2005h:11265)
  • [Ber05] L. Berger.
    Représentations modulaires de $ \operatorname{GL}_2(\mathbf{Q}_p)$ et représentations galoisiennes de dimension $ 2$,
    To appear in Astérisque.
  • [BB06] L Berger and C. Breuil.
    Sur quelques représentations potentiellement cristallines de $ \operatorname{GL}_2(\mathbf{Q}_p)$,
    To appear in Astérisque.
  • [Bre01] C. Breuil.
    Lectures on $ p$-adic Hodge theory, deformations and local Langlands, Volume 20, Advanced course lecture notes.
    Centre de Recerca Matemàtica, Barcelona (2001).
  • [Bre03] C. Breuil.
    Sur quelques représentations modulaires et $ p$-adiques de $ \operatorname{GL}_2(\mathbf{Q}_p)$ II,
    J. Inst. Math. Jussieu, 2 (2003), 23-58. MR 1955206 (2005d:11079)
  • [Bre04] C. Breuil.
    Invariant $ \mathcal{L}$ et série spéciale $ p$-adique,
    Ann. Scient. de l'École Norm. Sup., 37 (2004), 559-610. MR 2097893 (2005j:11039)
  • [BCDT] C. Breuil, B. Conrad, F. Diamond and R. Taylor.
    On the modularity of elliptic curves over $ \mathbf{Q}$: wild $ 3$-adic exercices,
    J. Amer. Soc, 14 (2001), 843-939. MR 1839918 (2002d:11058)
  • [BE05] C. Breuil and M. Emerton.
    Représentations $ p$-adiques ordinaires de $ \operatorname{GL}_2(\mathbf{Q}_p)$ et compatibilité local-global,
    To appear in Astérisque.
  • [BM02] C. Breuil and A. Mézard.
    Multiplicités modulaires et représentations de $ \operatorname{GL}_2(\mathbf{Z}_p)$ et de $ \operatorname{Gal}(\bar{\mathbf{Q}}_p/\mathbf{Q}_p)$ en $ l=p$,
    Duke Math. J., 115 (2002), 205-310. MR 1944572 (2004i:11052)
  • [BM05] C. Breuil and A. Mézard.
    Représentations semi-stables de $ \operatorname{Gl}_2(\mathbf{Q}_p)$, demi-plan $ p$-adique et réduction modulo $ p$,
    To appear in Astérisque.
  • [Col04] P. Colmez.
    Une correspondance de Langlands locale $ p$-adique pour les représentations semi-stables de dimension $ 2$,
    To appear in Astérisque.
  • [Col05] P. Colmez.
    Série principale unitaire pour $ \operatorname{GL}_2(\mathbf{Q}_p)$ et représentations triangulines de dimension $ 2$,
    To appear in Astérisque.
  • [Col07] P. Colmez.
    La série principale unitaire de $ \operatorname{GL}_2(\mathbf{Q}_p)$,
    To appear in Astérisque.
  • [CF00] P. Colmez and J.-M. Fontaine.
    Construction des représentations p-adiques semi-stables,
    Invent. Math., 140 (2000), 1-43. MR 1779803 (2001g:11184)
  • [Eme05] M. Emerton.
    $ p$-adic $ L$-functions and unitary completions of representations of $ p$-adic reductive groups,
    Duke Math. J, 130 (2005), 353-392. MR 2181093 (2007e:11058)
  • [Fon94a] J.-M. Fontaine.
    Représentations p-adiques semi-stables,
    Astérisque, 223, Soc. Math. de France (1994), 113-184. MR 1293972 (95g:14024)
  • [Fon94b] J.-M. Fontaine.
    Le corps des périodes p-adiques,
    Astérisque, 223, Soc. Math. de France (1994), 59-111. MR 1293971 (95k:11086)
  • [FM95] J.-M. Fontaine and B. Mazur.
    Geometric Galois representations.
    In Elliptic curves, modular forms, & Fermat's last theorem.
    Proceedings of the conference on elliptic curves and modular forms held at the Chinese University of Hong Kong, December 18-21, 1993.
    International Press. Ser. Number Theory. 1, 41-78 (1995). MR 1363495 (96h:11049)
  • [GV04] E. Ghate and V. Vatsal.
    On the local behaviour of ordinary $ \Lambda$-adic representations,
    Ann. Inst. Fourier (Grenoble), 54 (2004), 2143-2162. MR 2139691 (2006b:11050)
  • [GV07] E. Ghate and V. Vatsal.
    Locally indecomposable Galois representations,
    To appear in Canad. J. Math.
  • [Iwa86] K. Iwasawa.
    Local class field theory, volume 1400 of Oxford Science Publications. Oxford Mathematical Monographs.
    The Clarendon Press, Oxford University Press, New York, 1986. MR 863740 (88b:11080)
  • [Maz94] B. Mazur.
    On monodromy invariants occurring in global arithmetic, and Fontaine's theory.
    In $ p$-adic monodromy and the Birch and Swinnerton-Dyer conjecture (Boston, MA, 1991), volume 165 of Contemp. Math., pages 1-20. Amer. Math. Soc., Providence, RI, 1994. MR 1279599 (95e:11069)
  • [Miy89] T. Miyake.
    Modular Forms.
    Springer-Verlag, 1989. MR 1021004 (90m:11062)
  • [Sav05] D. Savitt.
    On a conjecture of Conrad, Diamond and Taylor,
    Duke Math. J., 128 (2005), 141-197. MR 2137952 (2006c:11060)
  • [Vol01] M. Volkov.
    Les représentations $ \ell$-adiques associées aux courbes elliptiques sur $ \mathbb{Q}_p$.
    J. Reine Angew. Math., 535:65-101, 2001. MR 1837096 (2002d:11067)

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Additional Information

Eknath Ghate
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
Email: eghate@math.tifr.res.in

Ariane Mézard
Affiliation: Laboratoire de mathématiques, Faculté des sciences d’Orsay, Université de Paris-Sud 11, 91405 Orsay Cedex, France
Address at time of publication: Laboratoire de Mathématiques de Versailles, Université de Versailles Saint-Quentin, 45 avenue des États Unis, 78035 Versailles, France
Email: mezard@math.uvsq.fr

DOI: https://doi.org/10.1090/S0002-9947-08-04829-0
Received by editor(s): May 8, 2006
Published electronically: December 15, 2008
Article copyright: © Copyright 2008 American Mathematical Society

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