Mordell-Weil growth for GL2-type abelian varieties over Hilbert class fields of CM fields

نویسنده

  • David Hansen
چکیده

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 .

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Nonvanishing of Hecke L–functions for Cm Fields and Ranks of Abelian Varieties

In this paper we prove a nonvanishing theorem for central values of L– functions associated to a large class of algebraic Hecke characters of CM number fields. A key ingredient in the proof is an asymptotic formula for the average of these central values. We combine the nonvanishing theorem with work of Tian and Zhang [TZ] to deduce that infinitely many of the CM abelian varieties associated to...

متن کامل

L-functions with Large Analytic Rank and Abelian Varieties with Large Algebraic Rank over Function Fields

The goal of this paper is to explain how a simple but apparently new fact of linear algebra together with the cohomological interpretation of L-functions allows one to produce many examples of L-functions over function fields vanishing to high order at the center point of their functional equation. Conjectures of Birch and Swinnerton-Dyer, Bloch, and Beilinson relate the orders of vanishing of ...

متن کامل

Selmer groups and Mordell-Weil groups of elliptic curves over towers of function fields

In [12] and [13], Silverman discusses the problem of bounding the Mordell-Weil ranks of elliptic curves over towers of function fields. We first prove generalizations of the theorems of those two papers by a different method, allowing non-abelian Galois groups and removing the dependence on Tate’s conjectures. We then prove some theorems about the growth of Mordell-Weil ranks in towers of funct...

متن کامل

The Selmer Group, the Shafarevich-tate Group, and the Weak Mordell-weil Theorem

This is an introduction to classical descent theory, in the context of abelian varieties over number fields.

متن کامل

A 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 کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010