Skip to main content
SpringerLink
Log in

The values of J-invariants for Drinfeld modules

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract.

Potemine defined in [8] J-invariants for Drinfeld modules of arbitrary rank. In this paper, we investigate the values of J-invariants of Drinfeld modules. In particular, using them, we construct class fields over a ``totally imaginary extension'' of đť”˝ q (T).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Deligne, P., Husemöller, D.: Survey of Drinfeld modules. Contemp. Math. 67, 25–91 (1987)

    MATH  Google Scholar 

  2. Drinfeld, V.G.: Elliptic modules. Math. USSR Sbornik 23, 561–592 (1974)

    MATH  Google Scholar 

  3. Gekeler, E.-U.: Zur Arithmetik von Drinfeld-Moduln. Math. Ann. 262, 167–182 (1983)

    MathSciNet  MATH  Google Scholar 

  4. Goss, D.: π-adic Eisenstein series for function fields. Compositio Math. 41, 3–38 (1980)

    MathSciNet  MATH  Google Scholar 

  5. Goss, D.: Modular forms for F r [T]. J. reine angew. math. 317, 16–39 (1980)

    MathSciNet  MATH  Google Scholar 

  6. Goss, D.: Basic Structures of Function Field Arithmetic. Springer, 1996

  7. Hayes, D.: Explicit class field theory in global function fields. In: G.-C. Rota (ed.), Studies in Algebra and Number Theory. New York: Academic Press, 1979, pp. 173–217

  8. Potemine, I.Y.: Minimal terminal ℚ-factorial models of Drinfeld coarse moduli schemes. Math. Phys. Anal. Geom. 1, 171–191 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  9. Rosen, M.: The Hilbert class field in function fields. Expo. Math. 5, 365–378 (1987)

    MathSciNet  MATH  Google Scholar 

  10. Schweizer, A.: On singular and supersingular invariants of Drinfeld modules. Ann. Fac. Sci. Toulouse 6, 319–334 (1997)

    MathSciNet  MATH  Google Scholar 

  11. Shimura, G.: Introduction to the Arithmetic Theory of Automorphic Functions. Iwanami Shoten Publishers and Princeton University Press, 1971

  12. Takahashi, T.: Good reduction of elliptic modules. J. Math. Soc. Japan 34, 475–487 (1982)

    MathSciNet  MATH  Google Scholar 

  13. Yu, J.: Transcendence and Drinfeld modules. Invent. math. 83, 507–517 (1986)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Tokyo University of Science, Noda, Chiba, 278-8510, Japan

    Yoshinori Hamahata

Authors
  1. Yoshinori Hamahata
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yoshinori Hamahata.

Additional information

Mathematics Subject Classification (2000): Primary 11G09; Secondary 10D25, 12A65, 12A90

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hamahata, Y. The values of J-invariants for Drinfeld modules. manuscripta math. 112, 93–108 (2003). https://doi.org/10.1007/s00229-003-0394-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00229-003-0394-0

Keywords

Search

Navigation