L-functions with large analytic rank and abelian varieties with large algebraic rank over function fields
Number Theory
2009-11-11 v1 Algebraic Geometry
Abstract
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. The main application is that for every prime p and every integer g>0 there are absolutely simple abelian varieties of dimension g over Fp(t) for which the BSD conjecture holds and which have arbitrarily large rank.
Cite
@article{arxiv.math/0609664,
title = {L-functions with large analytic rank and abelian varieties with large algebraic rank over function fields},
author = {Douglas Ulmer},
journal= {arXiv preprint arXiv:math/0609664},
year = {2009}
}
Comments
To appear in Inventiones Mathematicae