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2016 Furstenberg sets and Furstenberg schemes over finite fields
Jordan Ellenberg, Daniel Erman
Algebra Number Theory 10(7): 1415-1436 (2016). DOI: 10.2140/ant.2016.10.1415

Abstract

We give a lower bound for the size of a subset of Fqn 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 nonreduced subschemes and flat families to derive combinatorial facts about incidences between points and k-planes in space.

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Jordan Ellenberg. Daniel Erman. "Furstenberg sets and Furstenberg schemes over finite fields." Algebra Number Theory 10 (7) 1415 - 1436, 2016. https://doi.org/10.2140/ant.2016.10.1415

Information

Received: 20 April 2015; Revised: 3 May 2016; Accepted: 13 June 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1354.13033
MathSciNet: MR3554237
Digital Object Identifier: 10.2140/ant.2016.10.1415

Subjects:
Primary: 14G15
Secondary: 13P10, 42B25, 51E20

Rights: Copyright © 2016 Mathematical Sciences Publishers

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Vol.10 • No. 7 • 2016
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