Galois descent and twists of an abelian variety

Masanari Kida

Acta Arithmetica (1995)

  • Volume: 73, Issue: 1, page 51-57
  • ISSN: 0065-1036

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Masanari Kida. "Galois descent and twists of an abelian variety." Acta Arithmetica 73.1 (1995): 51-57. <http://eudml.org/doc/206809>.

@article{MasanariKida1995,
author = {Masanari Kida},
journal = {Acta Arithmetica},
keywords = {Galois descent; -series; isogeny; abelian variety; Weil restriction; twist; Mordell-Weil rank},
language = {eng},
number = {1},
pages = {51-57},
title = {Galois descent and twists of an abelian variety},
url = {http://eudml.org/doc/206809},
volume = {73},
year = {1995},
}

TY - JOUR
AU - Masanari Kida
TI - Galois descent and twists of an abelian variety
JO - Acta Arithmetica
PY - 1995
VL - 73
IS - 1
SP - 51
EP - 57
LA - eng
KW - Galois descent; -series; isogeny; abelian variety; Weil restriction; twist; Mordell-Weil rank
UR - http://eudml.org/doc/206809
ER -

References

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  1. [1] G. Faltings, Finiteness theorems for abelian varieties over number fields, in: Arithmetic Geometry, G. Cornell and J. H. Silverman (eds.), Springer, 1986, 9-27. Zbl0602.14044
  2. [2] T. Honda, Isogenies, rational points and section points of group varieties, Japan. J. Math. 30 (1960), 84-101. Zbl0109.39602
  3. [3] M. Kida, On the rank of an elliptic curve in elementary 2-extensions, Proc. Japan Acad. 69 (1993), 422-425. Zbl0824.14027
  4. [4] J. S. Milne, On the arithmetic of abelian varieties, Invent. Math. 17 (1972), 177-190. Zbl0249.14012
  5. [5] J. S. Milne, Abelian varieties, in: Arithmetic Geometry, G. Cornell and J. H. Silverman (eds.), Springer, 1986, 103-150. Zbl0604.14028
  6. [6] J. Neukirch, Class Field Theory, Springer, 1986. Zbl0587.12001
  7. [7] T. Ono, On the relative Mordell-Weil rank of elliptic quartic curves, J. Math. Soc. Japan 32 (1980), 665-670. Zbl0456.14013
  8. [8] I. Satake, Classification Theory of Semi-simple Algebraic Groups, Marcel Dekker, New York, 1971. Zbl0226.20037
  9. [9] A. Sato, The behavior of Mordell-Weil groups under field extensions, preprint. 
  10. [10] J.-P. Serre, Représentations linéaires des groupes finis, deuxième éd., Hermann, Paris, 1971. 
  11. [11] A. Weil, Adeles and Algebraic Groups, Birkhäuser, 1982 Zbl0118.15801

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