• Martin L. BrownEmail author
Part of the Lecture Notes in Mathematics book series (LNM, volume 1849)


  • Appendix A. Rigid analytic modular forms
    • A.1. Basic definitions

    • A.2. The Tate algebra

    • A.3. Affinoid spaces, rigid analytic spaces

    • A.4. Etale cohomology of rigid analytic spaces

    • A.5. The space \(\Omega^d\)

    • A.6. The moduli scheme M d I

    • A.7. An analytic description of M d I

    • A.8. Rigid analytic modular forms

    • A.9. Analytic modular forms

    • A.10. q-expansions at the cusps of \({\overline M}^2_I\)

    • A.11. Eisenstein series

    • A.12. Hecke operators

    • A.13. Elliptic curves over F and modular forms

  • Appendix B. Automorphic forms and elliptic curves over function fields
    • B.1. The Bruhat-Tits building for PGL over a local field

    • B.2. The building map on \(\Omega^d\)

    • B.3. Fibres of the building map on \(\Omega^2\)

    • B.4. Structures of level H on Drinfeld modules; the moduli scheme M d H

    • B.5. Action of arithmetic subgroups of \({\rm GL}_2(F)\) on T

    • B.6. Cohomology of \(\Omega^2\) and harmonic cochains

    • B.7. Cohomology of the moduli space M2 H

    • B.8. Harmonic cochains and the special representation of \({\rm GL}_2( F_\infty )\)

    • B.9. Automorphic forms and the main theorem

    • B.10. The Langlands correspondence \(\pi \to \sigma (\pi )\)

    • B.11. Elliptic curves as images of Drinfeld modular curves

    • B.12. The Langlands conjecture for GL n over function fields (according to Lafforgue)

Mathematics Subject Classification (2000):

11F52 11G05 11G09 11G15 11G40 11R58 14F20 14G10 14H52 14J27 14K22 


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Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  1. 1.Institut FourierSaint-Martin d’HèresFrance

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