ScholarLens Back to search
2019•arXiv (Cornell University)Open access

Ranks of abelian varieties and the full Mordell-Lang conjecture in\n dimension one

Arno Fehm, Sebastian Petersen

Open full text 0 citations

Abstract

Let $A$ be a non-zero abelian variety over a field $F$ that is not algebraic\nover a finite field. We prove that the rational rank of the abelian group\n$A(F)$ is infinite when $F$ is large in the sense of Pop (also called ample).\nThe main ingredient is a deduction of the 1-dimensional case of the relative\nMordell-Lang conjecture from a result of R\\"ossler.\n

Open-access reader

About this research paper

What this paper is about

Let $A$ be a non-zero abelian variety over a field $F$ that is not algebraic\nover a finite field. We prove that the rational rank of the abelian group\n$A(F)$ is infinite when $F$ is large in the sense of Pop (also called ample).\nThe main ingredient is a deduction of the 1-dimensional case of the relative\nMordell-Lang conjecture from a result of R\\"ossler.\n

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Let $A$ be a non-zero abelian variety over a field $F$ that is not algebraic\nover a finite field. We prove that the rational rank of the abelian group\n$A(F)$ is infinite when $F$ is large in the sense of Pop (also called ample).\nThe main ingredient is a deduction of the 1-dimensional case of the relative\nMordell-Lang conjecture from a result of R\\"ossler.\n

Key concepts: Abelian group, Arithmetic of abelian varieties, Mathematics, Conjecture, Abelian variety, Rank of an abelian group, Rank (graph theory), Dimension (graph theory)

Related papers

Related paper 1Related paper 2
Back to paper searchBrowse research topicsOriginal source
Ranks of abelian varieties and the full Mordell-Lang conjecture in\n dimension one — Research Paper | ScholarLens