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arXiv · 1502.03736

Furstenberg sets and Furstenberg schemes over finite fields

Jordan S. Ellenberg·Daniel Erman
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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.

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Jordan S. Ellenberg, Daniel Erman. 2015-02-12. Furstenberg sets and Furstenberg schemes over finite fields. https://doi.org/10.2140/ant.2016.10.1415

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