Bourgain-type projection theorems over finite fields

TL;DR

This paper establishes finite-field versions of Bourgain's projection theorem, improving exceptional set estimates across various dimensions and codimensions in higher-dimensional finite fields.

Contribution

It introduces finite-field analogs of Bourgain's projection theorem and enhances previous exceptional set bounds in multiple dimensions.

Findings

Improved bounds on exceptional sets in finite fields.

Extended Bourgain's projection theorem to higher dimensions.

Achieved better estimates across all dimensions and codimensions.

Abstract

We prove finite-field analogs of Bourgain's projection theorem in higher dimensions. In particular, for a certain range of parameters we improve on an exceptional set estimate by Chen in all dimensions and codimensions.