Restricted families of projections in vector spaces over finite fields

TL;DR

This paper investigates specific families of projections in finite field vector spaces, demonstrating that certain random subspace families satisfy a projection theorem analogous to Marstrand-Mattila's in Euclidean spaces.

Contribution

It introduces and analyzes restricted families of projections in finite fields, establishing conditions under which a Marstrand-Mattila type theorem holds.

Findings

Existence of random subspace families satisfying projection theorems

Extension of Euclidean projection results to finite fields

Conditions for Marstrand-Mattila type theorems in finite field settings

Abstract

We study the restricted families of projections in vector spaces over finite fields. We show that there are families of random subspaces which admit a Marstrand-Mattila type projection theorem.