Skip to Main Content

Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Local indecomposability of Tate modules of non-CM abelian varieties with real multiplication
HTML articles powered by AMS MathViewer

by Haruzo Hida PDF
J. Amer. Math. Soc. 26 (2013), 853-877 Request permission


Indecomposability of $p$-adic Tate modules over the $p$-inertia group for non-CM (partially $p$-ordinary) abelian varieties with real multiplication is proven under unramifiedness of $p$ in the base field and in the multiplication field.
  • David Mumford, Abelian varieties, Tata Institute of Fundamental Research Studies in Mathematics, vol. 5, Published for the Tata Institute of Fundamental Research, Bombay; by Hindustan Book Agency, New Delhi, 2008. With appendices by C. P. Ramanujam and Yuri Manin; Corrected reprint of the second (1974) edition. MR 2514037
  • Goro Shimura, Abelian varieties with complex multiplication and modular functions, Princeton Mathematical Series, vol. 46, Princeton University Press, Princeton, NJ, 1998. MR 1492449, DOI 10.1515/9781400883943
  • Jean-Pierre Serre, Abelian $l$-adic representations and elliptic curves, Research Notes in Mathematics, vol. 7, A K Peters, Ltd., Wellesley, MA, 1998. With the collaboration of Willem Kuyk and John Labute; Revised reprint of the 1968 original. MR 1484415
  • Gary Cornell and Joseph H. Silverman (eds.), Arithmetic geometry, Springer-Verlag, New York, 1986. Papers from the conference held at the University of Connecticut, Storrs, Connecticut, July 30–August 10, 1984. MR 861969, DOI 10.1007/978-1-4613-8655-1
  • N. Bourbaki, Algébre, Hermann, Paris, 1958.
  • Kevin Buzzard, Fred Diamond, and Frazer Jarvis, On Serre’s conjecture for mod $\ell$ Galois representations over totally real fields, Duke Math. J. 155 (2010), no. 1, 105–161. MR 2730374, DOI 10.1215/00127094-2010-052
  • G. Banaszak, W. Gajda, and P. Krasoń, On Galois representations for abelian varieties with complex and real multiplications, J. Number Theory 100 (2003), no. 1, 117–132. MR 1971250, DOI 10.1016/S0022-314X(02)00121-X
  • Siegfried Bosch and Werner Lütkebohmert, Formal and rigid geometry. I. Rigid spaces, Math. Ann. 295 (1993), no. 2, 291–317. MR 1202394, DOI 10.1007/BF01444889
  • Brian Conrad, Several approaches to non-Archimedean geometry, $p$-adic geometry, Univ. Lecture Ser., vol. 45, Amer. Math. Soc., Providence, RI, 2008, pp. 9–63. MR 2482345, DOI 10.1090/ulect/045/02
  • A. J. de Jong, Crystalline Dieudonné module theory via formal and rigid geometry, Inst. Hautes Études Sci. Publ. Math. 82 (1995), 5–96 (1996). MR 1383213
  • A. J. De Jong, Erratum to: “Crystalline Dieudonné module theory via formal and rigid geometry” Inst. Hautes Études Sci. Publ. Math. No. 87 (1998), 175.
  • Sigurdur Helgason, Differential geometry, Lie groups, and symmetric spaces, Pure and Applied Mathematics, vol. 80, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 514561
  • M. Emerton, A $p$-adic variational Hodge conjecture and modular forms with complex multiplication, preprint
  • H. Hida, Elliptic Curves and Arithmetic Invariants, Springer Monographs in Mathematics, to be published in 2013.
  • A. Grothendieck and J. Dieudonné, Eléments de Géométrie Algébrique, Publications IHES 4 (1960), 8 (1961), 11 (1961), 17 (1963), 20 (1964), 24 (1965), 28 (1966), 32 (1967).
  • David Mumford, Geometric invariant theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 34, Springer-Verlag, Berlin-New York, 1965. MR 0214602
  • Eknath Ghate, Ordinary forms and their local Galois representations, Algebra and number theory, Hindustan Book Agency, Delhi, 2005, pp. 226–242. MR 2193355
  • Eknath Ghate and Vinayak Vatsal, On the local behaviour of ordinary $\Lambda$-adic representations, Ann. Inst. Fourier (Grenoble) 54 (2004), no. 7, 2143–2162 (2005) (English, with English and French summaries). MR 2139691
  • B. Balasubramanyam, E. Ghate and V. Vatsal, On local Galois representations attached to ordinary Hilbert modular forms, preprint 2012
  • Haruzo Hida, Geometric modular forms and elliptic curves, 2nd ed., World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2012. MR 2894984
  • Haruzo Hida, Automorphism groups of Shimura varieties, Doc. Math. 11 (2006), 25–56. MR 2226268
  • Haruzo Hida, The Iwasawa $\mu$-invariant of $p$-adic Hecke $L$-functions, Ann. of Math. (2) 172 (2010), no. 1, 41–137. MR 2680417, DOI 10.4007/annals.2010.172.41
  • Haruzo Hida, Constancy of adjoint $\scr L$-invariant, J. Number Theory 131 (2011), no. 7, 1331–1346. MR 2782844, DOI 10.1016/j.jnt.2011.02.001
  • Haruzo Hida, Irreducibility of the Igusa tower over unitary Shimura varieties, On certain $L$-functions, Clay Math. Proc., vol. 13, Amer. Math. Soc., Providence, RI, 2011, pp. 187–203. MR 2767517
  • Goro Shimura, Introduction to the arithmetic theory of automorphic functions, Kanô Memorial Lectures, No. 1, Iwanami Shoten Publishers, Tokyo; Princeton University Press, Princeton, N.J., 1971. Publications of the Mathematical Society of Japan, No. 11. MR 0314766
  • N. Katz, Serre-Tate local moduli, Algebraic surfaces (Orsay, 1976–78) Lecture Notes in Math., vol. 868, Springer, Berlin-New York, 1981, pp. 138–202. MR 638600
  • Nicholas M. Katz, $p$-adic $L$-functions for CM fields, Invent. Math. 49 (1978), no. 3, 199–297. MR 513095, DOI 10.1007/BF01390187
  • Toshitsune Miyake, On automorphism groups of the fields of automorphic functions, Ann. of Math. (2) 95 (1972), 243–252. MR 300977, DOI 10.2307/1970798
  • Rutger Noot, Abelian varieties—Galois representation and properties of ordinary reduction, Compositio Math. 97 (1995), no. 1-2, 161–171. Special issue in honour of Frans Oort. MR 1355123
  • S. Bosch, U. Güntzer, and R. Remmert, Non-Archimedean analysis, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 261, Springer-Verlag, Berlin, 1984. A systematic approach to rigid analytic geometry. MR 746961, DOI 10.1007/978-3-642-52229-1
  • A. Ogus, Hodge cycles and crystalline cohomology, in: Hodge Cycles, Motives, and Shimura Varieties, Chapter VI, Lecture Notes in Math. 900 (1982), 357–414.
  • Haruzo Hida, $p$-adic automorphic forms on Shimura varieties, Springer Monographs in Mathematics, Springer-Verlag, New York, 2004. MR 2055355, DOI 10.1007/978-1-4684-9390-0
  • M. Rapoport, Compactifications de l’espace de modules de Hilbert-Blumenthal, Compositio Math. 36 (1978), no. 3, 255–335 (French). MR 515050
  • Kenneth A. Ribet, Galois action on division points of Abelian varieties with real multiplications, Amer. J. Math. 98 (1976), no. 3, 751–804. MR 457455, DOI 10.2307/2373815
  • Jean-Pierre Serre, Quelques applications du théorème de densité de Chebotarev, Inst. Hautes Études Sci. Publ. Math. 54 (1981), 323–401 (French). MR 644559
  • Goro Shimura, On canonical models of arithmetic quotients of bounded symmetric domains, Ann. of Math. (2) 91 (1970), 144–222. MR 257031, DOI 10.2307/1970604
  • J. T. Tate, $p$-divisible groups, Proc. Conf. Local Fields (Driebergen, 1966) Springer, Berlin, 1967, pp. 158–183. MR 0231827
  • B. Zhao, Local indecomposability of Hilbert modular Galois representations, preprint, 2012 (posted in web: arXiv:1204.4007v1 [math.NT])
Similar Articles
Additional Information
  • Haruzo Hida
  • Affiliation: Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095-1555
  • MR Author ID: 213427
  • Email:
  • Received by editor(s): April 1, 2012
  • Received by editor(s) in revised form: December 27, 2012
  • Published electronically: March 18, 2013
  • Additional Notes: The author is partially supported by NSF grants DMS 0753991 and DMS 0854949
  • © Copyright 2013 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 26 (2013), 853-877
  • MSC (2010): Primary 14G35, 11G15, 11G18, 11F80; Secondary 11G10, 14L05
  • DOI:
  • MathSciNet review: 3037789