Towers of GL($r$)-type of modular curves

References

[1] G. W. Anderson, t-motives, Duke Math. J. 53 (1986), no. 2, 457–502. 10.1215/S0012-7094-86-05328-7Search in Google Scholar

[2] A. Bassa, Talk at the conference the arithmetic of function fields (Busan 2013). Search in Google Scholar

[3] A. Bassa, P. Beelen, A. Garcia and H. Stichtenoth, Towers of function fields over non-prime finite fields, Mosc. Math. J. 15 (2015), no. 1, 1–29, 181 10.17323/1609-4514-2015-15-1-1-29Search in Google Scholar

[4] S. Bosch, U. Güntzer and R. Remmert, Non-Archimedean analysis. A systematic approach to rigid analytic geometry, Grundlehren Math. Wiss. 261, Springer, Berlin 1984. 10.1007/978-3-642-52229-1Search in Google Scholar

[5] P. Deligne and D. Husemoller, Survey of Drinfel’d modules, Current trends in arithmetical algebraic geometry (Arcata 1985), Contemp. Math. 67, American Mathematical Society, Providence (1987), 25–91. 10.1090/conm/067/902591Search in Google Scholar

[6] P. Deligne and M. Rapoport, Les schémas de modules de courbes elliptiques, Modular functions of one variable. II (Antwerp 1972), Lecture Notes in Math. 349, Springer, Berlin (1973), 143–316. 10.1007/978-3-540-37855-6_4Search in Google Scholar

[7] V. G. Drinfel’d, Elliptic modules (Russian), Mat. Sb. (N.S.) 94(136) (1974), 594–627, 656. 10.1070/SM1974v023n04ABEH001731Search in Google Scholar

[8] J. Fresnel and M. van der Put, Rigid analytic geometry and its applications, Progr. Math. 218, Birkhäuser, Boston 2004. 10.1007/978-1-4612-0041-3Search in Google Scholar

[9] E.-U. Gekeler, Drinfel’d-Moduln und modulare Formen über rationalen Funktionenkörpern, Bonn. Math. Schr. 119 (1980), 1–142. Search in Google Scholar

[10] E.-U. Gekeler, Modulare Einheiten für Funktionenkörper, J. reine angew. Math. 348 (1984), 94–115. 10.1515/crll.1984.348.94Search in Google Scholar

[11] E.-U. Gekeler, Drinfeld modular curves, Lecture Notes in Math. 1231, Springer, Berlin 1986. 10.1007/BFb0072692Search in Google Scholar

[12] E.-U. Gekeler, Über Drinfeldsche Modulkurven vom Hecke-Typ, Compos. Math. 57 (1986), no. 2, 219–236. Search in Google Scholar

[13] E.-U. Gekeler, On the coefficients of Drinfeld modular forms, Invent. Math. 93 (1988), no. 3, 667–700. 10.1007/BF01410204Search in Google Scholar

[14] E.-U. Gekeler, On finite Drinfeld modules, J. Algebra 141 (1991), no. 1, 187–203. 10.1016/0021-8693(91)90211-PSearch in Google Scholar

[15] E.-U. Gekeler, Finite modular forms, Finite Fields Appl. 7 (2001), no. 4, 553–572. 10.1006/ffta.2000.0314Search in Google Scholar

[16] E.-U. Gekeler, Invariants of some algebraic curves related to Drinfeld modular curves, J. Number Theory 90 (2001), no. 1, 166–183. 10.1006/jnth.2000.2642Search in Google Scholar

[17] E.-U. Gekeler and U. Nonnengardt, Fundamental domains of some arithmetic groups over function fields, Internat. J. Math. 6 (1995), no. 5, 689–708. 10.1142/S0129167X95000286Search in Google Scholar

[18] E.-U. Gekeler and M. Reversat, Jacobians of Drinfeld modular curves, J. reine angew. Math. 476 (1996), 27–93. 10.1515/crll.1996.476.27Search in Google Scholar

[19] L. Gerritzen and M. van der Put, Schottky groups and Mumford curves, Lecture Notes in Math. 817, Springer, Berlin 1980. 10.1007/BFb0089957Search in Google Scholar

[20] D. Goss, Modular forms for Fr⁢[T], J. reine angew. Math. 317 (1980), 16–39. 10.1515/crll.1980.317.16Search in Google Scholar

[21] D. Goss, π-adic Eisenstein series for function fields, Compos. Math. 41 (1980), no. 1, 3–38. Search in Google Scholar

[22] D. Goss, Basic structures of function field arithmetic, Ergeb. Math. Grenzgeb. (3) 35, Springer, Berlin 1996. 10.1007/978-3-642-61480-4Search in Google Scholar

[23] R. Hartshorne, Algebraic geometry, Grad. Texts in Math. 52, Springer, New York 1977. 10.1007/978-1-4757-3849-0Search in Google Scholar

[24] D. R. Hayes, Explicit class field theory for rational function fields, Trans. Amer. Math. Soc. 189 (1974), 77–91. 10.1090/S0002-9947-1974-0330106-6Search in Google Scholar

[25] Y. Ihara, Some remarks on the number of rational points of algebraic curves over finite fields, J. Fac. Sci. Univ. Tokyo Sect. I A Math. 28 (1981), no. 3, 721–724. Search in Google Scholar

[26] W. M. Kantor, Linear groups containing a Singer cycle, J. Algebra 62 (1980), no. 1, 232–234. 10.1016/0021-8693(80)90214-8Search in Google Scholar

[27] R. Kiehl, Der Endlichkeitssatz für eigentliche Abbildungen in der nichtarchimedischen Funktionentheorie, Invent. Math. 2 (1967), 191–214. 10.1007/BF01425513Search in Google Scholar

[28] R. Kiehl, Theorem A und Theorem B in der nichtarchimedischen Funktionentheorie, Invent. Math. 2 (1967), 256–273. 10.1007/BF01425404Search in Google Scholar

[29] J. Neukirch, Algebraic number theory, Grundlehren Math. Wiss. 322, Springer, Berlin 1999. 10.1007/978-3-662-03983-0Search in Google Scholar

[30] R. Pink, Compactification of Drinfeld modular varieties and Drinfeld modular forms of arbitrary rank, Manuscripta Math. 140 (2013), no. 3–4, 333–361. 10.1007/s00229-012-0544-3Search in Google Scholar

[31] R. Pink and S. Schieder, Compactification of a Drinfeld period domain over a finite field, J. Algebraic Geom. 23 (2014), no. 2, 201–243. 10.1090/S1056-3911-2013-00605-0Search in Google Scholar

[32] P. Schneider and U. Stuhler, The cohomology of p-adic symmetric spaces, Invent. Math. 105 (1991), no. 1, 47–122. 10.1007/BF01232257Search in Google Scholar

[33] J.-P. Serre, Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier (Grenoble) 6 (1955/1956), 1–42. 10.1007/978-3-642-39816-2_32Search in Google Scholar

[34] J.-P. Serre, Corps locaux, Act. Sci. Indust. 1296, Hermann & Cie, Paris 1962. Search in Google Scholar

[35] Y. Taguchi, Semi-simplicity of the Galois representations attached to Drinfel’d modules over fields of “infinite characteristics”, J. Number Theory 44 (1993), no. 3, 292–314. 10.1006/jnth.1993.1055Search in Google Scholar

[36] M. A. Tsfasman and S. G. Vlǎduţ, Algebraic-geometric codes, Math. Appl. (Soviet Series) 58, Kluwer Academic Publishers, Dordrecht 1991. 10.1007/978-94-011-3810-9Search in Google Scholar

[37] M. A. Tsfasman, S. G. Vlǎduţ and T. Zink, Modular curves, Shimura curves, and Goppa codes, better than Varshamov–Gilbert bound, Math. Nachr. 109 (1982), 21–28. 10.1002/mana.19821090103Search in Google Scholar

[38] G. van der Geer and M. van der Vlugt, Tables of curves with many points, Math. Comp. 69 (2000), no. 230, 797–810. 10.1090/S0025-5718-99-01143-6Search in Google Scholar