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AN INCIDENCE CONJECTURE OF BOURGAIN OVER FIELDS OF POSITIVE CHARACTERISTIC

Part of: Discrete geometry Algebraic geometry: Foundations

Published online by Cambridge University Press:  30 August 2016

JORDAN S. ELLENBERG  and
MÁRTON HABLICSEK
JORDAN S. ELLENBERG
Affiliation:
Department of Mathematics, University of Wisconsin, 325 Van Vleck Hall, 480 Lincoln Drive, Madison, WI 53706, USA; ellenber@math.wisc.edu
MÁRTON HABLICSEK
Affiliation:
Department of Mathematics, University of Pennsylvania, David Rittenhouse Lab., 209 South 33rd Street, Philadelphia, PA 19104-6395, USA; mhabli@math.upenn.edu

Abstract

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In this note we generalize a recent theorem of Guth and Katz on incidences between points and lines in 3-space from characteristic 0 to characteristic $p$, and we explain how some of the special features of algebraic geometry in characteristic $p$ manifest themselves in problems of incidence geometry.

MSC classification

Primary: 52C10: Erdős problems and related topics of discrete geometry
Secondary: 14A25: Elementary questions
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 4 , 2016 , e23
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2016

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