A subspace theorem for manifolds

TL;DR

This paper generalizes Schmidt's Subspace Theorem within metric diophantine approximation by employing homogeneous dynamics, slope formalism, and semistability concepts for diagonal flows.

Contribution

It introduces a new reformulation of the Subspace Theorem using homogeneous dynamics, slope formalism, and semistability for diagonal flows.

Findings

Established a generalized subspace theorem for manifolds

Developed a slope formalism for diagonal flows

Connected diophantine approximation with homogeneous dynamics

Abstract

We prove a theorem that generalizes Schmidt's Subspace Theorem in the context of metric diophantine approximation. To do so we reformulate the Subspace theorem in the framework of homogeneous dynamics by introducing and studying a slope formalism and the corresponding notion of semistability for diagonal flows.