A functorial lower bound for the essential minimum of varities in a power of an elliptic curve

TL;DR

This paper establishes a new, sharp lower bound for the essential minimum of non-translate subvarieties within powers of an elliptic curve, advancing understanding in diophantine geometry.

Contribution

It introduces a functorial approach to derive a lower bound for the essential minimum of non-translate subvarieties in powers of elliptic curves, improving previous bounds.

Findings

Proves a sharp lower bound for the essential minimum of non-translate subvarieties.

Extends known bounds to a broader class of subvarieties in elliptic curve powers.

Provides a functorial method for deriving bounds in diophantine geometry.

Abstract

A subvariety V of an abelian variety is `translate' if it is the union of translates of proper algebraic subgroups. An irreducible V is `transverse' if it is not contained in any translate variety. Effective sharp lower bounds for a transverse subvarieties of a power of an elliptic curve E are known. Here, we prove a sharp lower bound for the essential minimum of non-translate subvarieties of such a power E^g.