Multiplier ideal sheaves, Nevanlinna theory, and diophantine approximation

TL;DR

This paper proposes a new conjecture linking Nevanlinna theory and diophantine approximation through multiplier ideal sheaves, offering a potentially more convenient formulation that is equivalent to existing conjectures.

Contribution

It introduces a reformulation of key conjectures using multiplier ideal sheaves, which may simplify applications despite not providing new results.

Findings

Conjecture is equivalent to existing ones in Nevanlinna theory and diophantine approximation.

Uses a correction term involving multiplier ideal sheaves.

Provides a potentially more convenient formulation for applications.

Abstract

This note states a conjecture for Nevanlinna theory or diophantine approximation, with a sheaf of ideals in place of the normal crossings divisor. This is done by using a correction term involving a multiplier ideal sheaf. This new conjecture trivially implies earlier conjectures in Nevanlinna theory or diophantine approximation, and in fact is equivalent to these conjectures. Although it does not provide anything new, it may be a more convenient formulation for some applications.