English

Furstenberg sets and Furstenberg schemes over finite fields

Algebraic Geometry 2016-10-05 v1 Classical Analysis and ODEs Combinatorics

Abstract

We give a lower bound for the size of a subset of Fqn\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.

Keywords

Cite

@article{arxiv.1502.03736,
  title  = {Furstenberg sets and Furstenberg schemes over finite fields},
  author = {Jordan S. Ellenberg and Daniel Erman},
  journal= {arXiv preprint arXiv:1502.03736},
  year   = {2016}
}

Comments

16 pages

R2 v1 2026-06-22T08:28:34.163Z