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...
متن کاملSome remarks on almost rational torsion points par
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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A billiard ball, i.e. a point mass, moves inside a polygon Q with unit speed along a straight line until it reaches the boundary ∂Q of the polygon, then instantaneously changes direction according to the mirror law: “the angle of incidence is equal to the angle of reflection,” and continues along the new line (Fig. 1(a)). Despite the simplicity of this description there is much that is unknown ...
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1. Recurrent and almost periodic transformations. Notations. Let ƒ be a continuous mapping (not necessarily a homeomorphism) of a topological space X in itself (that is, f(X)QX). We say that ƒ is recurrent a t a point # £ X , or that x is recurrent under ƒ, if, given any neighbourhood U(x) of x, there exist infinitely many positive integers n for which f(x)ÇE.U(x). (This definition is equivalen...
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We study the number of rational points of bounded height on a certain threefold. The accumulating subvarieties are Zariski-dense in this example. The computations support an extension of a conjecture of Manin to this situation.
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 1999
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.1999.v6.n5.a3