Furstenberg sets and Furstenberg schemes over finite fields

Jordan S. Ellenberg, Daniel Erman

Type: Article

Publication Date: 2016-09-27

Citations: 6

DOI: https://doi.org/10.2140/ant.2016.10.1415

Abstract

We give a lower bound for the size of a subset of $\mathbb F_q^n$ containing a rich k-plane in every direction, a k-plane Furstenberg set. The chief novelty of our method is that we use arguments on non-reduced subschemes and flat families to derive combinatorial facts about incidences between points and k-planes in space.

Locations

Algebra & Number Theory - View - PDF
arXiv (Cornell University) - View - PDF
Project Euclid (Cornell University) - View - PDF
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