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
โฆ LIBER โฆ
On the Twist of Abelian Varieties Defined by the Galois Extension of Prime Degree
โ Scribed by W.B. Wang
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 132 KB
- Volume
- 163
- Category
- Article
- ISSN
- 0021-8693
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Let p be an odd prime and n a positive integer and let k be a field of ลฝ . r p and let r denote the largest integer between 0 and n such that K l k s p ลฝ . r r r k , where denotes a primitive p th root of unity. The extension Krk is p p separable, but not necessarily normal and, by Greither and Pa