We prove the indecomposability of the Galois representation restricted to the -decomposition group attached to a non CM nearly -ordinary weight two Hilbert modular form over a totally real field under the assumption that either the degree of over is odd or the automorphic representation attached to the Hilbert modular form is square integrable at some finite place of .
Nous prouvons l’indécomposabilité de la représentation galoisienne restreinte au groupe de -décomposition attaché à une forme modulaire quasi-ordinaire de Hilbert sans multiplication complexe de poids sous certainess hypothèses.
Keywords: Galois representation, Hilbert modular forms, complex multiplication
Mot clés : Représentation galoisienne, formes modulaires de Hilbert, multiplication complexe
Zhao, Bin 1
@article{AIF_2014__64_4_1521_0, author = {Zhao, Bin}, title = {Local {Indecomposability} of {Hilbert} {Modular} {Galois} {Representations}}, journal = {Annales de l'Institut Fourier}, pages = {1521--1560}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {64}, number = {4}, year = {2014}, doi = {10.5802/aif.2889}, mrnumber = {3329672}, zbl = {06387316}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2889/} }
TY - JOUR AU - Zhao, Bin TI - Local Indecomposability of Hilbert Modular Galois Representations JO - Annales de l'Institut Fourier PY - 2014 SP - 1521 EP - 1560 VL - 64 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2889/ DO - 10.5802/aif.2889 LA - en ID - AIF_2014__64_4_1521_0 ER -
%0 Journal Article %A Zhao, Bin %T Local Indecomposability of Hilbert Modular Galois Representations %J Annales de l'Institut Fourier %D 2014 %P 1521-1560 %V 64 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2889/ %R 10.5802/aif.2889 %G en %F AIF_2014__64_4_1521_0
Zhao, Bin. Local Indecomposability of Hilbert Modular Galois Representations. Annales de l'Institut Fourier, Volume 64 (2014) no. 4, pp. 1521-1560. doi : 10.5802/aif.2889. https://aif.centre-mersenne.org/articles/10.5802/aif.2889/
[1] On local Galois representations associated to ordinary Hilbert modular forms (Preprint)
[2] Anticyclotomic -adic -function of central critical Rankin-Selberg -value (IMRN. doi:10.1093/imrn/rnq275)
[3] Sur les représentations l-adiques associées aux formes modulaires de Hilbert, Ann. Sci. École Norm. Sup. (4), Volume 19 (1986), pp. 409-468 | Numdam | MR | Zbl
[4] Classical and overconvergent modular forms, Invent. Math., Volume 124 (1996) no. 1-3, pp. 215-241 | DOI | MR | Zbl
[5] CM Liftings, 2011
[6] Jacobians with complex multiplication, Arithmetic Algebraic Geometry (Progress in Math.), Volume 89, Brikhäuser, Boston, 1991, pp. 177-192 | Zbl
[7] Singularités des espaces de modules de Hilbert, en les caractéristiques divisant le discriminant, Compositio Math., Volume 90 (1994), pp. 59-79 | Numdam | MR | Zbl
[8] A -adic variational Hodge conjecture and modular forms with complex multiplication (preprint available at Emerton’s homepage: http://www.math.uchicago.edu/~emerton/pdffiles/cm.pdf)
[9] Finiteness theorems for abelian varieties over number fields, Arithmetic geometry, Springer-Verlag, New York, 1986, pp. 9-27 | MR | Zbl
[10] Ordinary forms and their local Galois representations, Algebra and number theory, Hindustan Book Agency, Delhi, 2005, pp. 226-242 | MR | Zbl
[11] On the local behaviour of ordinary -adic representations, Ann. Inst. Fourier (Grenoble), Volume 54 (2004), pp. 2143-2162 | DOI | Numdam | MR | Zbl
[12] Lectures on Hilbert Modular Varieties and Modular Forms, CRM monograph series, American Mathematical Soc., 2001 no. 14 | MR | Zbl
[13] Families of modular eigenforms, Math. Comp., Volume 58 (1992) no. 198, pp. 793-805 | DOI | MR | Zbl
[14] Elliptic Curves and Arithmetic Invariant (book manuscript to be published by Springer)
[15] Local indecomposability of Tate modules of non CM abelian varieties with real multiplication (to appear in J. Amer. Math. Soc., preprint available at Hida’s homepage: http://www.math.ucla.edu/~hida/AbNSS.pdf) | MR | Zbl
[16] On abelian varieties with complex multiplication as factors of the Jacobians of Shimura curves, Amer. J. Math., Volume 103 (1981), pp. 727-776 | DOI | MR | Zbl
[17] On -adic Hecke algebras for over totally real fields, Ann. of Math., Volume 128 (1988), pp. 295-384 | DOI | MR | Zbl
[18] Nearly ordinary Hecke algebras and Galois representations of several variables, Algebraic analysis, geometry, and number theory (Baltimore, MD, 1988), Johns Hopkins Univ. Press, Baltimore, MD, 1989, pp. 115-134 | MR | Zbl
[19] On nearly ordinary Hecke algebras for over totally real fields, Algebraic number theory, Adv. Stud. Pure Math., 17, Academic Press, Boston, MA, 1989, pp. 139-169 | MR | Zbl
[20] p-adic automouphism forms on Shimura varieties, Springer Monographs in Mathematics, Springer-Verlag, 2004 | MR | Zbl
[21] Hilbert modular forms and Iwasawa theory, Oxford Mathematical Monographs, Oxford University Press, 2006 | MR | Zbl
[22] The Iwasawa -invariant of -adic Hecke -functions, Ann. of Math., Volume 172 (2010), pp. 41-137 | DOI | MR | Zbl
[23] Geometric Modular Forms and Elliptic Curves, World Scientific, Singapore, 2012 | MR | Zbl
[24] -adic properties of modular schemes and modular forms, Modular functions of one variable III (Lecture Notes in Math.), Volume 350, Springer, Berlin, 1973, pp. 69-190 | MR | Zbl
[25] -adic -functions for CM fields, Invent. Math., Volume 49 (1978), pp. 199-297 | DOI | MR | Zbl
[26] Serre-Tate local moduli, Algebraic surfaces (Orsay, 1976-78) (Lecture Notes in Math.), Volume 868, Springer, Berlin-New York, 1981, pp. 138-202 | MR | Zbl
[27] Geometric Invariant Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Neue Folge, 34, Springer-Verlag, Berlin-New York, 1965 | MR | Zbl
[28] An analytic construction of degenerating abelian varieties over complete rings, Compositio Math., Volume 24 (1972), pp. 239-272 | Numdam | MR | Zbl
[29] Compactifications de l’espace de modules de Hilbert-Blumenthal, Compositio Math., Volume 36 (1978) no. 3, pp. 255-335 | Numdam | MR | Zbl
[30] Galois action on division points of abelian varieties with real multiplications, Amer. J. Math., Volume 98 (1976), pp. 751-804 | DOI | MR | Zbl
[31] Good reduction of abelian varieties, Ann. of Math., Volume 88 (1965), pp. 492-517 | DOI | MR | Zbl
[32] On analytic families of polarized abelian varieties and automorphic functions, Ann. of Math., Volume 78 (1963), pp. 149-192 | DOI | MR | Zbl
[33] Number theoretic background, Automorphic forms, representations and L-functions (1977), pp. 3-26 (part 2) | MR | Zbl
[34] On -adic representations for totally real fields, Ann. of Math., Volume 123 (1986), pp. 407-456 | DOI | MR | Zbl
[35] On ordinary -adic representations associated to modular forms, Invent. math., Volume 94 (1988), pp. 529-573 | DOI | MR | Zbl
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