The Rank of Abelian Varieties over Infin
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Michael Rosen; Siman Wong
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Article
📅
2002
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Elsevier Science
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English
⚖ 151 KB
asked if every Abelian variety A defined over a number field k with dim A > 0 has infinite rank over the maximal Abelian extension k ab of k. We verify this for the Jacobians of cyclic covers of P 1 , with no hypothesis on the Weierstrass points or on the base field. We also derive an infinite rank