Mapping Incidences

Details Mapping Incidences Mapping Incidences

2007-11-28

arxiv.org/abs/0711.4407v2

Mathematics

Combinatorics

15 pages, to appear in the Journal of the London Mathematical Society. Section 3 on Erd\H{o}s distance problem from the previo

Scientific paper

10.1112/jlms/jdr017

We show that any finite set S in a characteristic zero integral domain can be
mapped to the finite field of order p, for infinitely many primes p, preserving
all algebraic incidences in S. This can be seen as a generalization of the
well-known Freiman isomorphism lemma, and we give several combinatorial
applications (such as sum-product estimates).

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