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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A remark on kernels of reduction

Author: Robert F. Coleman
Journal: Proc. Amer. Math. Soc. 104 (1988), 699-701
MSC: Primary 11G10; Secondary 14K15
MathSciNet review: 964845
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Abstract: We show the group of torsion points on an Abelian variety defined over an algebraic closure of the rationals, $ {\mathbf{\bar Q}}$ is generated by the kernels of reduction of all the primes of $ {\mathbf{\bar Q}}$.

References [Enhancements On Off] (What's this?)

  • [F] G. Faltings, Enlicheitsätz für Abelsche Varietäten über Zahlkörpern, Invent. Math. 74 (1983), 349-366. MR 718935 (85g:11026a)
  • [Z] Yu G. Zarhin, A finiteness theorem for unpolarized Abelian varieties over number fields with prescribed places of bad reduction, Invent. Math. 79 (1985), 309-321. MR 778130 (86d:14041)

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Article copyright: © Copyright 1988 American Mathematical Society

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