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
Extensions of abelian varieties defined over a number field
β Scribed by Matthew A. Papanikolas; Niranjan Ramachandran
- Publisher
- Elsevier Science
- Year
- 2005
- Tongue
- English
- Weight
- 255 KB
- Volume
- 112
- Category
- Article
- ISSN
- 0022-314X
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β¦ Synopsis
We study the arithmetic aspects of the finite group of extensions of abelian varieties defined over a number field. In particular, we establish relations with congruences between modular forms and special values of L-functions.
π SIMILAR VOLUMES
This paper was written at the University of Massachusetts at Amherst. We thank the working seminar on Shimura varieties there for patiently listening to us as we worked through these results. Our thanks also go to R. Schoof for his encouragement and suggestions, as well as to our anonymous (but inva
Let A be a supersingular abelian variety over a finite field k which is k-isogenous to a power of a simple abelian variety over k. Write the characteristic polynomial of the Frobenius endomorphism of A relative to k as f = g e for a monic irreducible polynomial g and a positive integer e. We show th
In this paper we study the characteristic polynomials and the rational point group structure of supersingular varieties of dimension two over finite fields. Meanwhile, we also list all L-functions of supersingular curves of genus two over β«ήβ¬ 2 and determine the group structure of their divisor clas