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The Rank of Jacobian Varieties over the Maximal Abelian Extensions of Number Fields: Towards the Frey-Jarden Conjecture

✍ Scribed by Sairaiji, Fumio; Yamauchi, Takuya


Book ID
119962343
Publisher
Canadian Mathematical Society
Year
2012
Tongue
English
Weight
164 KB
Volume
55
Category
Article
ISSN
0008-4395

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The Rank of Abelian Varieties over Infin
✍ Michael Rosen; Siman Wong πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 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