Skip to main content
SpringerLink
Log in

On certain reduction problems concerning abelian surfaces

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

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.

Institutional subscriptions

References

  1. Beauville, A.:Prym Varieties and the Schottky Problem, Inventiones. Math.41(1977), 149–196.

    Article  MATH  MathSciNet  Google Scholar 

  2. Deligne, P. and Mumford, D.:The Irreducibility of the Space of Curves of Given Genus, Publ. Math. I.H.E.S.36(1969), 75–109.

    MATH  MathSciNet  Google Scholar 

  3. DeShalit, E. and Goren, E.Z.:On Special Values of Theta Functions of Genus Two, Preprint, June 1996.

  4. Ekedahl, T.:On Supersingular Curves and Abelian Varieties, Math. Scand.60(1987), 151–178.

    MATH  MathSciNet  Google Scholar 

  5. Katsura, T. and Oort, F.:Families of Supersingular Abelian Surfaces, Compositio Math.62(1987), 107–167.

    MATH  MathSciNet  Google Scholar 

  6. Lang, S.:Complex Multiplication, Grundlehren der mathematischen Wissenschaften,225, Springer-Verlag, New-York, 1983.

    Google Scholar 

  7. Mumford, D.:Prym Varieties I, in: Contributions to Analysis, Academic Press, New York, 1974, 325–350.

    Google Scholar 

  8. Manin, Y.I.:The Theory of Commutative Formal Groups over Fields of Finite Characteristic, Russian Math. Surveys18(1963), 1–80.

    Article  MATH  MathSciNet  Google Scholar 

  9. Moret-Bailly, L.:Groupes de Picard et Problèmes de Skolem, Ann. Scient. Éc. Norm. Sup., 4e série, t.22, 1989, 181–194.

    MATH  MathSciNet  Google Scholar 

  10. Namikawa, Y. and Ueno, K.:The Complete Classification of Fibres in Pencils of Curves of Genus Two, Manuscripta Math.9(1973), 143–186.

    Article  MATH  MathSciNet  Google Scholar 

  11. Oort, F.:Which Abelian Surfaces are Products of Elliptic Curves?, Math. Ann.214(1975), 35–47.

    Article  MATH  MathSciNet  Google Scholar 

  12. Oort, F.:Moduli of Abelian Varieties in Positive Characteristic, In: Barsotti Symposium in Algebraic Geometry, Perspectives in Math.15, Academic Press, 1994, 253–276.

  13. Rumely, R.S.:Arithmetic over the ring of all algebriac integers, J. Reine Angew. Math.368(1986), 127–133.

    MATH  MathSciNet  Google Scholar 

  14. Shimura, G.:On the Zeta-function of an Abelian Variety with Complex Multiplication, Ann. of Math.94(1971), 504–533.

    Article  MathSciNet  Google Scholar 

  15. Serre, J.P. and Tate, J.:Good Reduction of Abelian Varieties, Ann. of Math.88(1968), 492–517.

    Article  MathSciNet  Google Scholar 

  16. Shimura, G. and Taniyama, Y.:Complex Multiplication of Abelian Varieties and its Application to Number Theory, Publ. Math. Soc. Japan6, 1961.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Harvard University, Science Center, One Oxford St., 02138, Cambridge, MA, USA

    Eyal Z. Goren

Authors
  1. Eyal Z. Goren
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Goren, E.Z. On certain reduction problems concerning abelian surfaces. Manuscripta Math 94, 33–43 (1997). https://doi.org/10.1007/BF02677837

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02677837

Keywords

Search

Navigation