Some remarks on almost rational torsion points
نویسندگان
چکیده
منابع مشابه
Some Remarks on Almost Rational Torsion Points
For a commutative algebraic group G over a perfect field k, Ribet defined the set of almost rational torsion points G tors,k of G over k. For positive integers d, g, we show there is an integer Ud,g such that for all tori T of dimension at most d over number fields of degree at most g, T ar tors,k ⊆ T [Ud,g]. We show the corresponding result for abelian varieties with complex multiplication, an...
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Let G be a commutative algebraic group defined over a perfect field k. Let k be an algebraic closure of k and Γk be the Galois group of k over k. Following Ribet ([1], [19], see also [7]), we say a point P ∈ G(k) is almost rational over k if whenever σ, τ ∈ Γk are such that σ(P )+ τ(P ) = 2P , then σ(P ) = τ(P ) = P . We denote the almost rational points of G over k by Gar k . Let Gtors denote ...
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2006
ISSN: 1246-7405
DOI: 10.5802/jtnb.531