General information
Latest issue
Forthcoming papers
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Mat. Sb.:

Personal entry:
Save password
Forgotten password?

Mat. Sb. (N.S.), 1974, Volume 94(136), Number 4(8), Pages 594–627 (Mi msb3735)  

This article is cited in 75 scientific papers (total in 75 papers)

Elliptic modules

V. G. Drinfeld

Abstract: The notion of elliptic module is introduced, generalizing the concept of an elliptic curve, and an analog of the theory of elliptic and modular curves is constructed. Here the role of the group $GL(2,Q)$ is played by $GL(2,k)$, where $k$ is a function field. A theorem on the coincidence of $L$-functions of modular curves and Jacquet–Langlands $L$-functions corresponding to $k$ is proved.
Bibliography: 14 titles.

Full text: PDF file (3781 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1974, 23:4, 561–592

Bibliographic databases:

UDC: 519.49
MSC: Primary 10D25, 12A65; Secondary 14K22
Received: 17.12.1973

Citation: V. G. Drinfeld, “Elliptic modules”, Mat. Sb. (N.S.), 94(136):4(8) (1974), 594–627; Math. USSR-Sb., 23:4 (1974), 561–592

Citation in format AMSBIB
\by V.~G.~Drinfeld
\paper Elliptic modules
\jour Mat. Sb. (N.S.)
\yr 1974
\vol 94(136)
\issue 4(8)
\pages 594--627
\jour Math. USSR-Sb.
\yr 1974
\vol 23
\issue 4
\pages 561--592

Linking options:

    SHARE: FaceBook Twitter Livejournal

    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
    Cycle of papers

    This publication is cited in the following articles:
    1. V. G. Drinfeld, “Coverings of $p$-adic symmetric regions”, Funct. Anal. Appl., 10:2 (1976), 107–115  mathnet  crossref  mathscinet  zmath
    2. B. Mazur, “Modular curves and the Eisenstein ideal”, Publications Mathématiques de l’Institut des Hautes Études Scientifiques, 47:1 (1977), 33  crossref  mathscinet  zmath  adsnasa
    3. V. G. Drinfeld, “Elliptic modules. II”, Math. USSR-Sb., 31:2 (1977), 159–170  mathnet  crossref  mathscinet  zmath  isi
    4. V. G. Drinfeld, “Commutative subrings of certain noncommutative rings”, Funct. Anal. Appl., 11:1 (1977), 9–12  mathnet  crossref  mathscinet  zmath
    5. Kurihara A., “Construction of P-Adic Unit Balls and the Hirzebruch Proportionality”, Am. J. Math., 102:3 (1980), 565–648  crossref  isi
    6. Steven Galovich, Michael Rosen, “Units and class groups in cyclotomic function fields”, Journal of Number Theory, 14:2 (1982), 156  crossref
    7. Ernst-Ulrich Gekeler, “Automorphe Formen über Fq (T) mit kleinem Führer”, Abh Math Semin Univ Hambg, 55:1 (1985), 111  crossref  zmath
    8. Benedict H. Gross, “On canonical and quasi-canonical liftings”, Invent math, 84:2 (1986), 321  crossref  mathscinet  zmath  isi
    9. Ulrich Stuhler, “P-adic homogeneous spaces and moduli problems”, Math Z, 192:4 (1986), 491  crossref  mathscinet  zmath  isi
    10. M. M. Kapranov, “On cuspidal divisors on the modular varieties of elliptic modules”, Math. USSR-Izv., 30:3 (1988), 533–547  mathnet  crossref  mathscinet  zmath
    11. V. G. Drinfeld, “Varieties of modules of $F$-sheaves”, Funct. Anal. Appl., 21:2 (1987), 107–122  mathnet  crossref  mathscinet  zmath  isi
    12. Benedict Gross, Michael Rosen, “Fourier series and the special values of L-functions”, Advances in Mathematics, 69:1 (1988), 1  crossref
    13. Teitelbaum J., “Values of P-Adic l-Functions and a P-Adic Poisson Kernel”, Invent. Math., 101:2 (1990), 395–410  crossref  isi
    14. Ernst-Ulrich Gekele, “On finite Drinfeld modules”, Journal of Algebra, 141:1 (1991), 187  crossref
    15. Dinesh S. Thakur, “Gauss sums for function fields”, Journal of Number Theory, 37:2 (1991), 242  crossref
    16. Boutot J. Carayol H., “P-Adic Uniformization of Shimura Curves - Cerednik and Drinfeld Theorems”, Asterisque, 1991, no. 196-97, 45–158  isi
    17. Vladimir G. Berkovich, “Étale cohomology for non-Archimedean analytic spaces”, Publ Math Inst Hautes Étud Sci, 78:1 (1993), 5  crossref  mathscinet  zmath
    18. Yoshinori Hamahata, “Tensor products of Drinfeld modules andv-adic representations”, manuscripta math, 79:1 (1993), 307  crossref  mathscinet  zmath
    19. Laurent Denis, “Irrationalité de Valeurs Associées a l'Exponentielle de Carlitz”, Mh Math, 123:1 (1997), 43  crossref  mathscinet  zmath
    20. Bruno Angles, “On some characteristic polynomials attached to finite Drinfeld modules”, manuscripta math, 93:1 (1997), 369  crossref  mathscinet  zmath  isi
    21. Neil P. Strickland, “Finite subgroups of formal groups”, Journal of Pure and Applied Algebra, 121:2 (1997), 161  crossref
    22. Gunther Cornelissen, “Drinfeld Modular Forms of Weight One”, Journal of Number Theory, 67:2 (1997), 215  crossref
    23. Yakov Varshavsky, “ p-adic uniformization of unitary Shimura varieties”, Publications Mathématiques de l’Institut des Hautes Études Scientifiques, 87:1 (1998), 57  crossref  mathscinet  zmath
    24. Liang-chung Hsia, “On the Coefficients of Modular Polynomials for Drinfeld Modules”, Journal of Number Theory, 72:2 (1998), 236  crossref
    25. Liang-Chung Hsia, Jing Yu, “On Singular Moduli of Drinfeld Modules in Characteristic Two”, Journal of Number Theory, 69:1 (1998), 80  crossref
    26. Dinesh S. Thakur, “An Alternate Approach to Solitons for q[t]”, Journal of Number Theory, 76:2 (1999), 301  crossref
    27. C.-L. Chai, “Local monodromy for deformations of one-dimensional formal groups”, crll, 2000:524 (2000), 227  crossref  mathscinet  zmath
    28. Véronique Mauduit, “Euler Pseudoprime Polynomials and Strong Pseudoprime Polynomials”, Finite Fields and Their Applications, 6:3 (2000), 218  crossref
    29. A. Álvarez, “Drinfeld Moduli Schemes and Infinite Grassmannians”, Journal of Algebra, 225:2 (2000), 822  crossref
    30. Dinesh S. Thakur, “Integrable systems and number theory in finite characteristic”, Physica D: Nonlinear Phenomena, 152-153 (2001), 1  crossref
    31. Ernst-Ulrich Gekeler, “Invariants of Some Algebraic Curves Related to Drinfeld Modular Curves”, Journal of Number Theory, 90:1 (2001), 166  crossref
    32. John A Rhodes, “Automorphic Forms, Definite Quaternion Algebras, and Atkin–Lehner Theory on Trees”, Journal of Number Theory, 86:2 (2001), 210  crossref
    33. G. Faltings, “Group schemes with strict $\mathcal{O}$-action”, Mosc. Math. J., 2:2 (2002), 249–279  mathnet  mathscinet  zmath  elib
    34. Francis Gardeyn, “A Galois criterion for good reduction of τ-sheaves”, Journal of Number Theory, 97:2 (2002), 447  crossref
    35. Francis Gardeyn, “The structure of analytic τ-sheaves”, Journal of Number Theory, 100:2 (2003), 332  crossref
    36. Roland Gillard, Franck Leprevost, Alexei Panchishkin, Xavier-François Roblot, “Utilisation des modules de Drinfeld en cryptologie”, Comptes Rendus Mathematique, 336:11 (2003), 879  crossref
    37. Chia-Fu Yu, Jing Yu, “Mass formula for supersingular Drinfeld modules”, Comptes Rendus Mathematique, 338:12 (2004), 905  crossref
    38. S. V. Oblezin, “Isomonodromic deformations of $\mathfrak{sl}(2)$ Fuchsian systems on the Riemann sphere”, Mosc. Math. J., 5:2 (2005), 415–441  mathnet  mathscinet  zmath
    39. “ON THE GLOBAL MINIMAL DrinfelD MODULE EQUATIONS”, Bulletin of the Korean Mathematical Society, 42:3 (2005), 485  crossref
    40. A. Álvarez, “Generalized theta functions, Drinfeld modules and some arithmetic consequences”, Journal of Number Theory, 110:2 (2005), 279  crossref
    41. Hausberger T., “Uniformization of Laumon-Rapoport-Stuhler Varieties and Drinfeld-Carayol Conjecture”, Ann. Inst. Fourier, 55:4 (2005), 1285+  isi
    42. Hartl U., “Uniformizing the Stacks of Abelian Sheaves”, Number Fields and Function Fields - Two Parallel Worlds, Progress in Mathematics, 239, ed. VanDerGeer G. Moonen B. Schoof R., Birkhauser Boston, 2005, 167–222  isi
    43. Ambrus Pál, “Proof of an exceptional zero conjecture for elliptic curves over function fields”, Math Z, 254:3 (2006), 461  crossref  mathscinet  zmath  isi
    44. Hilmar Hauer, Ignazio Longhi, “Teitelbaum's exceptional zero conjecture in the function field case”, crll, 2006:591 (2006), 149  crossref  mathscinet  zmath
    45. Gert-Jan van der Heiden, “Drinfeld modular curve and Weil pairing”, Journal of Algebra, 299:1 (2006), 374  crossref
    46. Richard Pink, “The Galois representations associated to a Drinfeld module in special characteristic—I: Zariski density”, Journal of Number Theory, 116:2 (2006), 324  crossref
    47. LENNY TAELMAN, “DIEUDONNÉ DETERMINANTS FOR SKEW POLYNOMIAL RINGS”, J. Algebra Appl, 05:01 (2006), 89  crossref
    48. J.-F. Dat, “Théorie de Lubin-Tate non-abélienne et représentations elliptiques”, Invent math, 169:1 (2007), 75  crossref  mathscinet  zmath  adsnasa  isi
    49. Toby Gee, “Companion forms over totally real fields”, manuscripta math, 125:1 (2007), 1  crossref  mathscinet  isi
    50. AMBRUS PÁL, “ON THE Eisenstein IDEAL OF DrinfelD MODULAR CURVES”, Int. J. Number Theory, 03:04 (2007), 557  crossref
    51. Elena Mantovan, “A compactification of Igusa varieties”, Math Ann, 340:2 (2008), 265  crossref  mathscinet  zmath  isi
    52. M STRAUCH, “Deformation spaces of one-dimensional formal modules and their cohomology”, Advances in Mathematics, 217:3 (2008), 889  crossref
    53. Liang-Chung Hsia, “On the reduction of a non-torsion point of a Drinfeld module”, Journal of Number Theory, 128:6 (2008), 1458  crossref
    54. SINNOU DAVID, AMÍLCAR PACHECO, “LE PROBLÈME DE LEHMER ABÉLIEN POUR UN MODULE DE Drinfel'D”, Int. J. Number Theory, 04:06 (2008), 1043  crossref
    55. Mihran Papikian, “Modular varieties of �-elliptic sheaves and the Weil-Deligne bound”, crll, 2009:626 (2009), 115  crossref  zmath  isi
    56. Papikian M., “Endomorphisms of exceptional $\mathcal D$-elliptic sheaves”, Math. Z., 2009  crossref
    57. Matthias Bornhofen, Urs Hartl, “Pure Anderson motives over finite fields”, Journal of Number Theory, 129:2 (2009), 247  crossref
    58. Urs Hartl, “A dictionary between Fontaine-Theory and its analogue in equal characteristic”, Journal of Number Theory, 129:7 (2009), 1734  crossref
    59. Bornhofen M., Hartl U., “Pure Anderson motives and abelian $\tau$-sheaves”, Math. Z., 2010  crossref
    60. Ambrus Pál, “On the torsion of Drinfeld modules of rank two”, Journal für die reine und angewandte Mathematik (Crelles Journal), 2010:640 (2010), 1  crossref
    61. Yoichi Mieda, “Non-cuspidality outside the middle degree of ℓ-adic cohomology of the Lubin–Tate tower”, Advances in Mathematics, 225:4 (2010), 2287  crossref
    62. Matthias Strauch, “Galois actions on torsion points of one-dimensional formal modules”, Journal of Number Theory, 130:3 (2010), 528  crossref
    63. Jan Kohlhaase, “Admissible φ-modules and p-adic unitary representations”, Math. Z, 2011  crossref
    64. Mihran Papikian, “On Jacquet–Langlands isogeny over function fields”, Journal of Number Theory, 131:7 (2011), 1149  crossref
    65. Satoshi Kondo, Seidai Yasuda, “Zeta elements in the K-theory of Drinfeld modular varieties”, Math. Ann, 354:2 (2011), 529  crossref
    66. Chieh-Yu Chang, “On periods of the third kind for rank 2 Drinfeld module”, Math. Z, 2012  crossref
    67. Seunghwan Chang, Yoonjin Lee, “Galois characters arising from Drinfeld modules”, Journal of Number Theory, 2012  crossref
    68. Jan Kohlhaase, “On the Iwasawa theory of the Lubin–Tate moduli space”, Compositio Math, 2013, 1  crossref
    69. Bertrand Rémy, Amaury Thuillier, Annette Werner, “Automorphisms of Drinfeld half-spaces over a finite field”, Compositio Math, 2013, 1  crossref
    70. P. Ingram, “A Lower Bound for the Canonical Height Associated to a Drinfeld Module”, International Mathematics Research Notices, 2013  crossref
    71. Van Order J., “On the Dihedral Main Conjectures of Iwasawa Theory for Hilbert Modular Eigenforms”, Can. J. Math.-J. Can. Math., 65:2 (2013), 403–466  crossref  isi
    72. Masataka Chida, Satoshi Kondo, Takuya Yamauchi, “On the rational K 2 of a curve of GL2 type over a global field of positive characteristic”, J. K-Theory, 2014, 1  crossref
    73. A. W. Mason, Andreas Schweizer, “Elliptic points of the Drinfeld modular groups”, Math. Z, 2014  crossref
    74. Mihran Papikian, Fu-Tsun Wei, “On the Eisenstein ideal over function fields”, Journal of Number Theory, 2015  crossref
    75. Gebhard Böckle, Tommaso Centeleghe, “Hecke characters associated to Drinfeld modular forms”, Compositio Math, 2015, 1  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:3656
    Full text:1112
    First page:1

    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019