Galois descent and twists of an abelian variety

• Autorzy: Masanari Kida
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 73
• Numer: 1
• Strony: 51-57

Daty

wydano

1995

otrzymano

1994-12-05

poprawiono

1995-02-07

Twórcy

autor

Masanari Kida

• Department of Mathematical Sciences, Yamagata University, Yamagata, 990 Japan

Bibliografia

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