Arithmetic and geometry of the curve y³+1=x⁴

Matthew J. Klassen; Edward F. Schaefer

Acta Arithmetica (1996)

  • Volume: 74, Issue: 3, page 241-257
  • ISSN: 0065-1036

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Matthew J. Klassen, and Edward F. Schaefer. "Arithmetic and geometry of the curve y³+1=x⁴." Acta Arithmetica 74.3 (1996): 241-257. <http://eudml.org/doc/206850>.

@article{MatthewJ1996,
author = {Matthew J. Klassen, Edward F. Schaefer},
journal = {Acta Arithmetica},
keywords = {Jacobian variety; quartic curve; Weierstrass points; Mordell-Weil group; isogeny; CM elliptic curve},
language = {eng},
number = {3},
pages = {241-257},
title = {Arithmetic and geometry of the curve y³+1=x⁴},
url = {http://eudml.org/doc/206850},
volume = {74},
year = {1996},
}

TY - JOUR
AU - Matthew J. Klassen
AU - Edward F. Schaefer
TI - Arithmetic and geometry of the curve y³+1=x⁴
JO - Acta Arithmetica
PY - 1996
VL - 74
IS - 3
SP - 241
EP - 257
LA - eng
KW - Jacobian variety; quartic curve; Weierstrass points; Mordell-Weil group; isogeny; CM elliptic curve
UR - http://eudml.org/doc/206850
ER -

References

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  1. [C1] R. Coleman, Torsion points on curves and p-adic Abelian integrals, Ann. of Math. 121 (1985), 111-168. Zbl0578.14038
  2. [C2] R. Coleman, Torsion points on Abelian etale coverings of P¹-{0,1,∞}, Trans. Amer. Math. Soc. 311 (1989), 185-208. 
  3. [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. Zbl0100.03401
  4. [H] R. Hartshorne, Algebraic Geometry, Springer, New York, 1977. 
  5. [KS] M. J. Klassen and E. F. Schaefer, Group law and descent on smooth plane quartics, preprint. 
  6. [L] J. Lewittes, Automorphisms of compact Riemann surfaces, Amer. J. Math. 85 (1963), 734-752. Zbl0146.10403
  7. [Ma] A. Mattuck, Abelian varieties over p-adic ground fields, Ann. of Math. 62 (1955), 92-119. Zbl0066.02802
  8. [Mi] J. S. Milne, Jacobian varieties, in: Arithmetic Geometry, G. Cornell and J. H. Silverman (eds.), Springer, New York, 1986, 167-212. 
  9. [V] A. M. Vermeulen, Weierstrass points of weight two on curves of genus three, Ph.D. Thesis, University of Amsterdam, 1983. Zbl0534.14010

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