Arithmetic of cyclic quotients of the Fermat quintic

Pavlos Tzermias

Acta Arithmetica (1998)

  • Volume: 84, Issue: 4, page 375-384
  • ISSN: 0065-1036

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Pavlos Tzermias. "Arithmetic of cyclic quotients of the Fermat quintic." Acta Arithmetica 84.4 (1998): 375-384. <http://eudml.org/doc/207149>.

@article{PavlosTzermias1998,
author = {Pavlos Tzermias},
journal = {Acta Arithmetica},
keywords = {Fermat quintic curve; Jacobian; dual isogeny; Mordell-Weil group},
language = {eng},
number = {4},
pages = {375-384},
title = {Arithmetic of cyclic quotients of the Fermat quintic},
url = {http://eudml.org/doc/207149},
volume = {84},
year = {1998},
}

TY - JOUR
AU - Pavlos Tzermias
TI - Arithmetic of cyclic quotients of the Fermat quintic
JO - Acta Arithmetica
PY - 1998
VL - 84
IS - 4
SP - 375
EP - 384
LA - eng
KW - Fermat quintic curve; Jacobian; dual isogeny; Mordell-Weil group
UR - http://eudml.org/doc/207149
ER -

References

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  1. [1] R. Coleman:, Torsion points on abelian étale coverings of 𝐏¹ - {0,1,∞}, Trans. Amer. Math. Soc. 311 (1989), 185-208. 
  2. [2] R. Coleman:, Torsion points on Fermat curves, Compositio Math. 58 (1986), 191-208. Zbl0604.14019
  3. [3] D. Faddeev:, On the divisor class groups of some algebraic curves, Dokl. Akad. Nauk SSSR 136 (1961), 296-298 (in Russian); English transl.: Soviet Math. Dokl. 2 (1961), 67-69. 
  4. [4] D. Grant:, A proof of quintic reciprocity using the arithmetic of y = x⁵ + 1/4, Acta Arith. 75 (1996), 321-337. 
  5. [5] R. Greenberg:, On the Jacobian variety of some algebraic curves, Compositio Math. 42 (1981), 345-359. Zbl0475.14026
  6. [6] B. Gross: and D. Rohrlich, Some results on the Mordell-Weil group of the Jacobian of the Fermat curve, Invent. Math. 44 (1978), 201-224. Zbl0369.14011
  7. [7] N. Koblitz: and D. Rohrlich, Simple factors in the Jacobian of the Fermat curve, Canad. J. Math. 30 (1978), 1183-1205. Zbl0399.14023
  8. [8] M. Kurihara:, Some remarks on conjectures about cyclotomic fields and K-groups of Z, Compositio Math. 81 (1992), 223-236. Zbl0747.11055
  9. [9] C. Lim:, The geometry of the Jacobian of the Fermat curve of exponent five, J. Number Theory 41 (1991), 102-115. 
  10. [10] D. Prapavessi:, On the Jacobian of the Klein curve, Proc. Amer. Math. Soc. 122 (1994), 971-978. Zbl0823.14016
  11. [11] D. Rohrlich:, Points at infinity on the Fermat curves, Invent. Math. 39 (1977), 95-127. Zbl0357.14010
  12. [12] P. Tzermias:, Torsion points on Fermat Jacobians, Internat. Math. Res. Notices 1997, no. 2, 57-66. Zbl0906.11032

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