Analytical construction of Weil curves over function fields

Ernst-Ulrich Gekeler

Journal de théorie des nombres de Bordeaux (1995)

  • Volume: 7, Issue: 1, page 27-49
  • ISSN: 1246-7405

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Gekeler, Ernst-Ulrich. "Analytical construction of Weil curves over function fields." Journal de théorie des nombres de Bordeaux 7.1 (1995): 27-49. <http://eudml.org/doc/247648>.

@article{Gekeler1995,
author = {Gekeler, Ernst-Ulrich},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {degree of the Weil uniformization; Shimura-Taniyama-Weil conjecture; function fields; automorphic forms; normalized Hecke eigenform; Weil uniformization; strong Weil curve; valuation of the modular invariant},
language = {eng},
number = {1},
pages = {27-49},
publisher = {Université Bordeaux I},
title = {Analytical construction of Weil curves over function fields},
url = {http://eudml.org/doc/247648},
volume = {7},
year = {1995},
}

TY - JOUR
AU - Gekeler, Ernst-Ulrich
TI - Analytical construction of Weil curves over function fields
JO - Journal de théorie des nombres de Bordeaux
PY - 1995
PB - Université Bordeaux I
VL - 7
IS - 1
SP - 27
EP - 49
LA - eng
KW - degree of the Weil uniformization; Shimura-Taniyama-Weil conjecture; function fields; automorphic forms; normalized Hecke eigenform; Weil uniformization; strong Weil curve; valuation of the modular invariant
UR - http://eudml.org/doc/247648
ER -

References

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  1. [1] S. Bosch, W. Lütkebohmert and M. Raynaud, Néron models, Grundlehren. Math. Wiss., Springer, Berlin-New York, 1990. Zbl0705.14001MR1045822
  2. [2] P. Deligne, Formes modulaires et representations de GL(2). In: Modular Functions of One Variable II, Lect. Notes Math., vol. 349, Springer, BerlinHeidelbergNew York, 1974., pp. 55-105. Zbl0271.10032MR347738
  3. [3] P. Deligne and D. Husemöller, Survey of Drinfeld modules., Contemp. Math.67 (1987), 25-91. Zbl0627.14026MR902591
  4. [4] V.G. Drinfeld, Elliptic Modules, Math. Sbornik94 (1974), 594-627 (Russian); English Translation: Math. USSR-Sbornik23 (1976), 561-592. Zbl0321.14014MR384707
  5. [5] J. Fresnel et M. van der Put, Géométrie Analytique Rigide et Applications, Progr. Math., vol. 18, Birkhauser, BaselBoston, 1981. Zbl0479.14015MR644799
  6. [6] E.-U. Gekeler, Drinfeld-Moduln und modulare Formen über rationalen Funktionenkörpern, Bonner Math. Schriften119 (1980). Zbl0446.14018MR594434
  7. [7] E.-U. Gekeler, Automorphe Formen über Fq(T) mit kleinem Führer, Abh. Math. Sem. Univ. Hamburg55 (1985), 111-146. Zbl0564.10026MR831522
  8. [8] E.-U. Gekeler, Drinfeld Modular Curves, Lect. Notes Math., vol. 1231, Springer, BerlinHeidelbergNew York, 1986. Zbl0607.14020MR874338
  9. [9] E.-U. Gekeler, On the coefficients of Drinfeld modular forms, Invent. math. 93 (1988), 667-700. Zbl0653.14012MR952287
  10. [10] E.-U. Gekeler et M. Reversat, Jacobians of Drinfeld modular curves, submitted. Zbl0848.11029
  11. [11] L. Gerritzen, On non-archimedean representations of abelian varieties, Math. Ann.196 (1972), 323-346. Zbl0255.14013MR308132
  12. [12] L. Gerritzen and M. van der Put, Schottky Groups and Mumford Curves, Lect. Notes Math., vol. 817, Springer, BerlinHeidelbergNew York, 1980. Zbl0442.14009MR590243
  13. [13] O. Goldmann and N. Iwahori, The space of p-adic norms, Acta Math.109 (1963),137-177. Zbl0133.29402MR144889
  14. [14] D. Goss, π-adic Eisenstein Series for Function Fields, Comp. Math.41 (1980), 3-38. 
  15. [15] H. Jacquet and R.P. Langlands, Automorphic forms on GL(2), Lect. Notes Math., vol. 114, Springer, BerlinHeidelbergNew York, 1970. Zbl0236.12010MR401654
  16. [16] D. Mumford, An analytic construction of degenerating abelian varieties over complete rings, Comp. Math.24 (1972), 239-272. Zbl0241.14020MR352106
  17. [17] U. Nonnengardt, Arithmetisch definierte Graphen über rationalen Funktionenkörpern, Diplomarbeit, Saarbrücken (1994). 
  18. [18] W. Radtke, Diskontinuierliche Gruppen im Funktionenkörperfall, Dissertation, Bochum (1984). Zbl0572.14017
  19. [19] K. Ribet, Mod p Hecke operators and congruences between modular forms, Invent. Math.71 (1983), 193-205. Zbl0508.10018MR688264
  20. [20] A. Schweizer, Dissertation, in preparation. Zbl0508.94019
  21. [21] J.-P. Serre, Trees, Springer, Berlin- Heidelberg-New York, 1980. Zbl0548.20018MR607504
  22. [22] J. Tate, Algorithm for determining the type of a singular fiber in an elliptic pencil. Modular Functions of One Variable IV, Lect. Notes Math., vol. 476, Springer, BerlinHeidelbergNew York, 1975, pp. 33-52. Zbl1214.14020MR393039
  23. [23] J. Teitelbaum, Modular symbols for Fq(T), Duke Math. J. 68 (1992), 271-295. Zbl0777.11021MR1191561
  24. [24] A. Weil, Dirichlet series and automorphic forms, Lect. Notes Math., vol. 189, Springer, BerlinHeidelbergNew York, 1971. Zbl0218.10046
  25. [25] D. Zagier, Modular parametrizations of elliptic curves, Canad. Math. Bull.28 (1985), 372-384. Zbl0579.14027MR790959

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