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- W2150923210 abstract "For a commutative algebraic group G over a perfect field k, Ribet defined the set of almost rational torsion points G tors,k ar of G over k. For positive integers d, g, we show there is an integer U d,g such that for all tori T of dimension at most d over number fields of degree at most g, T tors,k ar ⊆T[U d,g ]. We show the corresponding result for abelian varieties with complex multiplication, and under an additional hypothesis, for elliptic curves without complex multiplication. Finally, we show that except for an explicit finite set of semi-abelian varieties G over a finite field k, G tors,k ar is infinite, and use this to show for any abelian variety A over a p-adic field k, there is a finite extension of k over which A tors,k ar is infinite." @default.
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- W2150923210 date "2006-01-01" @default.
- W2150923210 modified "2023-09-26" @default.
- W2150923210 title "Some remarks on almost rational torsion points" @default.
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- W2150923210 doi "https://doi.org/10.5802/jtnb.531" @default.
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