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manuscripta mathematica

, Volume 94, Issue 1, pp 33–43 | Cite as

On certain reduction problems concerning abelian surfaces

  • Eyal Z. Goren
Article

Keywords

Prime Ideal Elliptic Curve Complex Multiplication Elliptic Curf Abelian Variety 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [B]
    Beauville, A.:Prym Varieties and the Schottky Problem, Inventiones. Math.41(1977), 149–196.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [DM]
    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.zbMATHMathSciNetGoogle Scholar
  3. [DSG]
    DeShalit, E. and Goren, E.Z.:On Special Values of Theta Functions of Genus Two, Preprint, June 1996.Google Scholar
  4. [E]
    Ekedahl, T.:On Supersingular Curves and Abelian Varieties, Math. Scand.60(1987), 151–178.zbMATHMathSciNetGoogle Scholar
  5. [KO]
    Katsura, T. and Oort, F.:Families of Supersingular Abelian Surfaces, Compositio Math.62(1987), 107–167.zbMATHMathSciNetGoogle Scholar
  6. [L]
    Lang, S.:Complex Multiplication, Grundlehren der mathematischen Wissenschaften,225, Springer-Verlag, New-York, 1983.Google Scholar
  7. [M]
    Mumford, D.:Prym Varieties I, in: Contributions to Analysis, Academic Press, New York, 1974, 325–350.Google Scholar
  8. [Ma]
    Manin, Y.I.:The Theory of Commutative Formal Groups over Fields of Finite Characteristic, Russian Math. Surveys18(1963), 1–80.zbMATHCrossRefMathSciNetGoogle Scholar
  9. [MB]
    Moret-Bailly, L.:Groupes de Picard et Problèmes de Skolem, Ann. Scient. Éc. Norm. Sup., 4e série, t.22, 1989, 181–194.zbMATHMathSciNetGoogle Scholar
  10. [NU]
    Namikawa, Y. and Ueno, K.:The Complete Classification of Fibres in Pencils of Curves of Genus Two, Manuscripta Math.9(1973), 143–186.zbMATHCrossRefMathSciNetGoogle Scholar
  11. [O1]
    Oort, F.:Which Abelian Surfaces are Products of Elliptic Curves?, Math. Ann.214(1975), 35–47.zbMATHCrossRefMathSciNetGoogle Scholar
  12. [O2]
    Oort, F.:Moduli of Abelian Varieties in Positive Characteristic, In: Barsotti Symposium in Algebraic Geometry, Perspectives in Math.15, Academic Press, 1994, 253–276.Google Scholar
  13. [R]
    Rumely, R.S.:Arithmetic over the ring of all algebriac integers, J. Reine Angew. Math.368(1986), 127–133.zbMATHMathSciNetGoogle Scholar
  14. [S]
    Shimura, G.:On the Zeta-function of an Abelian Variety with Complex Multiplication, Ann. of Math.94(1971), 504–533.CrossRefMathSciNetGoogle Scholar
  15. [SeT]
    Serre, J.P. and Tate, J.:Good Reduction of Abelian Varieties, Ann. of Math.88(1968), 492–517.CrossRefMathSciNetGoogle Scholar
  16. [ST]
    Shimura, G. and Taniyama, Y.:Complex Multiplication of Abelian Varieties and its Application to Number Theory, Publ. Math. Soc. Japan6, 1961.Google Scholar

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Eyal Z. Goren
    • 1
  1. 1.Department of MathematicsHarvard University, Science CenterCambridgeUSA

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