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A remark on the rational points of Abelian varieties with values in cyclotomic \(\mathbb{Z}_p\)- extensions. (English) Zbl 0323.14010

MSC:
14G05 Rational points
14K15 Arithmetic ground fields for abelian varieties
11R18 Cyclotomic extensions
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[1] K. Iwasawa: On f-extensions of algebraic number fields. Bull. Amer. Math. Soc, 65, 183-226 (1959). · Zbl 0089.02402
[2] Ju. Manin: Cyclotomic fields and modular curves. Russ. Math. Surveys, 26,7-78 (1971). · Zbl 0266.14012
[3] B. Mazur: Rational points of abelian varieties with values in towers of number fields. Inventiones math., 18, 183-266 (1972). · Zbl 0245.14015
[4] D. Mumford: Abelian Varieties. Oxford Univ. Press, London (1970). · Zbl 0223.14022
[5] S. Sen: Lie algebras of Galois groups arising from Hodge-Tate modules. Ann. of Math., 07, 160-170 (1973). JSTOR: · Zbl 0258.12009
[6] J.-P. Serre: Abelian i-adic representations and elliptic curves. Benjamin Inc. New York (1968). · Zbl 0186.25701
[7] J.-P. Serre: Sur les groupes de Galois attaches aux groupes p-divisibles. Proceedings of a Conference on Local Fields, pp. 118-131. Springer, Berlin-Heidelberg-New York (1967). · Zbl 0189.02901
[8] J.-P. Serre and J. Tate: Good reduction of abelian varieties. Ann. of Math., 88, 492-517 (1968). JSTOR: · Zbl 0172.46101
[9] J. Tate: p-Divisible Groups. Proceedings of a Conference on Local Fields, pp. 158-183. Springer, Berlin-Heidelberg-New York (1967). · Zbl 0157.27601
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