Arithmetic and geometry of the curve y³+1=x⁴

• Autorzy: Matthew J. Klassen , Edward F. Schaefer
• Języki publikacji: EN

Kategorie tematyczne

• 14H45: Special curves and curves of low genus
• 11D25: Cubic and quartic equations
• 14H25: Arithmetic ground fields
• 11G30: Curves of arbitrary genus or genus ≠ 1 over global fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1996
• Tom: 74
• Numer: 3
• Strony: 241-257

Daty

wydano

1996

otrzymano

1995-04-20

poprawiono

1995-06-16

Twórcy

autor

Matthew J. Klassen

• Department of Mathematics, Santa Clara University, Santa Clara, California 95053, U.S.A.

autor

Edward F. Schaefer

• Department of Mathematics, Santa Clara University, Santa Clara, California 95053, U.S.A.

Bibliografia

• [C1] R. Coleman, Torsion points on curves and p-adic Abelian integrals, Ann. of Math. 121 (1985), 111-168.
• [C2] R. Coleman, Torsion points on Abelian etale coverings of P¹-{0,1,∞}, Trans. Amer. Math. Soc. 311 (1989), 185-208.
• [F] D. K. Faddeev, Group of divisor classes on the curve defined by the equation x⁴+y⁴=1, Soviet Math. Dokl. 1 (1960), 1149-1151.
• [H] R. Hartshorne, Algebraic Geometry, Springer, New York, 1977.
• [KS] M. J. Klassen and E. F. Schaefer, Group law and descent on smooth plane quartics, preprint.
• [L] J. Lewittes, Automorphisms of compact Riemann surfaces, Amer. J. Math. 85 (1963), 734-752.
• [Ma] A. Mattuck, Abelian varieties over p-adic ground fields, Ann. of Math. 62 (1955), 92-119.
• [Mi] J. S. Milne, Jacobian varieties, in: Arithmetic Geometry, G. Cornell and J. H. Silverman (eds.), Springer, New York, 1986, 167-212.
• [V] A. M. Vermeulen, Weierstrass points of weight two on curves of genus three, Ph.D. Thesis, University of Amsterdam, 1983.