Skip to main content

Part of the book series: Progress in Mathematics ((PM,volume 71))

Abstract

Sections 1–5 below form a description of joint work with W. McCallum [C-M]. Section 6 contains a sketch of an algorithm for computing the stable reduction of a cyclic p-covering of ℙl. Section 7 provides an example to which this algorithm is applied.

The erratum of this chapter is available at http://dx.doi.org/10.1007/978-1-4757-4267-1_15

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. G. Anderson.- Cyclotomic and a covering of the Taniyama group.

    Google Scholar 

  2. G. Anderson.- The hyperadellic gamma function (to appear).

    Google Scholar 

  3. F.A. Bogomolov.- Sur l'algébricité des représentations x-adiques, C.R. Acad. Sci. 290 (1980).

    Google Scholar 

  4. S. Bosch.- Formelle standard modellehyperelliptischer Kurven, Math. Ann. 251 (1980), 19 - 42.

    Article  MathSciNet  MATH  Google Scholar 

  5. S. Bosch, U. Guntzer and R. Remmert.- Non-Archimedian Analysis ( Springer-verlag, Berlin, 1984 ).

    Book  Google Scholar 

  6. S. Bosch and W. Lutkebohmert.- Stable reduction and uniformization of abelian varieties, I, Math. Ann.

    Google Scholar 

  7. R. Coleman.- The dilogarithm and the norm residue symbol, Bull. Math. Soc. France 109 (1981), 373 - 402.

    MATH  Google Scholar 

  8. R. Coleman and W. McCallum.- Stable reduction of Fermat curves and Jacobi sum Hecke characters, to appear.

    Google Scholar 

  9. P. Deligne and D. Mumford.- The irreducibility of the space of curves of a given genus, Publ. Math. IRES no 36 (1969), 75 - 109.

    MathSciNet  MATH  Google Scholar 

  10. B. Dwork and P. Robba.- On Natural R-adic of p-adic convergences. Trans. AMS, 256 (1979), 199 - 213.

    MathSciNet  MATH  Google Scholar 

  11. H. Hasse.- Zeta Funktion und L-funktionen zu einem arithmetishen funktionen - Körper vom fermatschen Typus, Abhand. der Deut. Akad. der Wissen zu berlin (1955).

    Google Scholar 

  12. C. Jensen.- Uber die FUhrer einer Klasse Heckeschen Grössencharakter, Math. Scand. 8 (1960), 151 - 165.

    Google Scholar 

  13. D. Kubert and S. Lichtenbaum.- Jacobi sum Hecke characters, Compositio Math. 48 (1983), 55 - 87.

    MathSciNet  MATH  Google Scholar 

  14. D. Kubert.- Jacobi sums and Hecke characters, Amer. J. Math. 107, No 2 (1985), 253 - 280.

    Article  MathSciNet  MATH  Google Scholar 

  15. D. Rohrlich.- Jacobi sums and explicit reciprocity laws, to appear in Comp. Math.

    Google Scholar 

  16. C.-G. Schmidt.- Uber die Fuhrer von Gausschen Summen als Grössencharactere, J. Number Theory 12 (1980), 283 - 310.

    Article  MathSciNet  MATH  Google Scholar 

  17. M. Vanderput.- Stable reductions of algebraic curves, to appear.

    Google Scholar 

  18. A. Weil.- Jacobi sums as Grössencharakter, Trans. Am. Math. Soc. 73 (1952), 487 - 495.

    MathSciNet  MATH  Google Scholar 

  19. A. Weil.- Sommes de Jacobi et caractères de Hecke, Gottingen Nachr. (1974), no 1.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer Science+Business Media New York

About this chapter

Cite this chapter

Coleman, R. (1987). Computing Stable Reductions. In: Goldstein, C. (eds) Séminaire de Théorie des Nombres, Paris 1985–86. Progress in Mathematics, vol 71. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-4267-1_1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-4267-1_1

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4757-4268-8

  • Online ISBN: 978-1-4757-4267-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics