# Schmidt's subspace theorem for moving hypersurface targets

## TL;DR

This paper establishes a Diophantine approximation analogue of a recent Second Main Theorem for moving hypersurfaces in projective varieties, inspired by the analogy with Nevanlinna theory and Vojta's dictionary.

## Contribution

It provides the first Diophantine approximation version of the Second Main Theorem for moving hypersurfaces, extending recent complex geometric results.

## Key findings

- Established a Diophantine analogue of the Second Main Theorem for moving hypersurfaces.
- Extended Vojta's dictionary to encompass moving targets in Diophantine approximation.
- Bridged a gap between complex Nevanlinna theory and number theory in the context of moving hypersurfaces.

## Abstract

It was discovered that there is a formal analogy between Nevanlinna theory and Diophantine approximation. Via Vojta's dictionary, the Second Main Theorem in Nevanlinna theory corresponds to Schmidt's Subspace Theorem in Diophantine approximation. Recently, Cherry, Dethloff, and Tan (arXiv:1503.08801v2 [math.CV]) obtained a Second Main Theorem for moving hypersurfaces intersecting projective varieites. In this paper, we shall give the counterpart of their Second Main Theorem in Diophantine approximation.