The number of curves of genus two with elliptic differentials

Journal fur die Reine und Angewandte Mathematik

Volumn 485, Issue , 1997, Pages 93-121

  Kani, Ernst ^a  

^a QUEEN S UNIVERSITY   (Canada)

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EID: 0031537202     PISSN: 00754102     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. O. Bolza, Über die Reduktion hyperelliptischer Integrale erster Ordnung und erster Gattung auf elliptische, insbesondere über die Reduktion durch eine Transformation vierten Grades, Inaugural Dissertation, Göttingen 1886.
2. G. Frey, On elliptic curves with isomorphic torsion structures and corresponding elliptic curves of genus 2, in: Elliptic Curves, Modular Forms and Fermat's Last Theorem (J. Coates, S. T. Yau, eds.), International Press Incorporated, Boston (1995), 79-98.
3. G. Frey, E. Kani, Curves of genus 2 covering elliptic curves and an arithmetical application, in: Arithmetic Algebraic Geometry (G. van der Geer, F. Oort, J. Steenbrink, eds.), Progr. Math. 89, Birkhäuser, Boston (1991), 153-176.
4. J. W. L. Glaisher, On the square of the series in which the coefficients are the sums of the divisors of the exponents, Mess. Math. 14 (1884/5), 156-163.
5. T. Hayashida, M. Nishi, Existence of curves of genus two on a product of two elliptic curves, J. Math. Soc. Japan 17 (1965), 1-16.
6. T. Ibukiyama, T. Katsura, F. Oort, Supersingular curves of genus two and class numbers, Comp. Math. 57 (1986), 127-152.
7. E. Kani, Curves with elliptic differentials, Preprint.
8. E. Kani, Curves of genus 2 with elliptic differentials and the height conjecture for elliptic curves, in: Proc. Conf. Number Theory and Arithmetic Geometry (G. Frey, ed.), Publ. Inst. Exp. Math. Essen, Preprint 18 (1991), 30-39.
9. E. Kani, Elliptic curves on abelian surfaces, Manuscr. math. 84 (1994), 199-223.
10. E. Kani, The existence of curves of genus 2 with elliptic differentials, J. Number Th., to appear.
11. A. Krazer, Lehrbuch der Thetafunktionen, Leipzig 1903 (Chelsea Reprint, 1970).
12. R. Kuhn, Curves of genus 2 with split Jacobian, Trans. Am. Math. Soc. 307 (1988), 41-49.
13. H. Lange, Über die Modulvarietät der Kurven vom Geschlecht 2, J. reine angew. Math. 281 (1976), 80-96.
14. H. Lange, Kurven mit rationaler Abbildung, J. reine angew. Math. 295 (1977), 80-115.
15. 1, II. Examples, in: Séminaire sur les pinceaux des courbes de genre au moins deux (L. Szpiro, ed.), Astérisque SMF 86 (1981), 125-140.
16. D. Mumford, Abelian Varieties, Oxford University Press, London 1970.
17. N. Murabayashi, The moduli space of curves of genus 2 covering elliptic curves, Manuscr. math. 84 (1994), 185-198.
18. T. Oda, The first DeRham cohomology group and Dieudonné modules, Ann. Sci. Éc. Norm. Sup. 2 (1969), 63-135.
19. F. Oort, Which abelian surfaces are products of elliptic curves? Math. Ann. 214 (1975), 35-47.
20. É. Picard, Sur la réduction du nombre des périodes des intégrales abéliennes et, en particulier, dans le cas des courbes du second genre, Bull. Soc. Math. France 11 (1883), 25-53.
21. J.-P. Serre, Groupes algébriques et corps de classes, Hermann, Paris 1958.
22. J.-P. Serre, Sur le nombre des points rationnels d'une courbe algébrique sur un corps fini, C. R. Acad. Sci. Paris 296 (1983), 397-402 = Oeuvres/Collected Papers III, pp. 658-663.
23. J.-P. Serre, Sur le nombre des points rationnels d'une courbe algébrique sur un corps fini, C. R. Acad. Sci. Paris 296 (1983), 397-402 = Oeuvres/Collected Papers III, pp. 658-663.
24. q, Sem. Th. Nombres Bordeaux 22 (1982/3) = Oeuvres/Collected Papers III, pp. 664-668.
25. q, Sem. Th. Nombres Bordeaux 22 (1982/3) = Oeuvres/Collected Papers III, pp. 664-668.
26. J. Silverman, The Arithmetic of Elliptic Curves, Springer-Verlag, New York 1986.
27. A. Weil, Zum Beweis des Torellischen Satzes, Göttinger Nachr. (1957), no. 2, 33-53 = Oeuvres Scientifiques/Collected Papers II, pp. 307-327.
28. A. Weil, Zum Beweis des Torellischen Satzes, Göttinger Nachr. (1957), no. 2, 33-53 = Oeuvres Scientifiques/Collected Papers II, pp. 307-327.