The Mordell-Weil group of certain abelian varieties defined over the rational function field
نویسندگان
چکیده
منابع مشابه
Mordell-Weil growth for GL2-type abelian varieties over Hilbert class fields of CM fields
Let A be a modular abelian variety of GL2-type over a totally real field F of class number one. Under some mild assumptions, we show that the Mordell-Weil rank of A grows polynomially over Hilbert class fields of CM extensions of F .
متن کاملOn the Mordell-weil Rank of an Abelian Variety over a Number Field
Let K be a number field and A an abelian variety over K. The K-rational points of A are known to constitute a finitely generated abelian group (Mordell-Weil theorem). The problem studied in this paper is to find an explicit upper bound for the rank r of its free part in terms of other invariants of A/K. This is achieved by a close inspection of the classical proof of the so-called ‘weak Mordell...
متن کاملA Mordell-weil Theorem for Abelian Varieties over Fields Generated by Torsion Points
Let A be an abelian variety over a number field, Tl the ladic Tate module, and Gl the image of the Galois action on Tl. Then Hi(Gl, Tl) is a finite l-group which vanishes for l ≫ 0. We apply this bound for i = 1 and i = 2 to show that ifK denotes the field generated by all torsion points of A, then A(K) is the direct sum of its torsion group and a free abelian group.
متن کاملAbelian Varieties and the Mordell–Lang Conjecture
This is an introductory exposition to background material useful to appreciate various formulations of the Mordell–Lang conjecture (now established by recent spectacular work due to Vojta, Faltings, Hrushovski, Buium, Voloch, and others). It gives an exposition of some of the elementary and standard constructions of algebro-geometric models (rather than model-theoretic ones) with applications (...
متن کاملChabauty without the Mordell-weil Group
Based on ideas from recent joint work with Bjorn Poonen, we describe an algorithm that can in certain cases determine the set of rational points on a curve C, given only the p-Selmer group S of its Jacobian (or some other abelian variety C maps to) and the image of the p-Selmer set of C in S. The method is more likely to succeed when the genus is large, which is when it is usually rather diffic...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1992
ISSN: 0040-8735
DOI: 10.2748/tmj/1178227300