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Preprint Number 5

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5 - Ehud Hrushovski and Frank Wagner
Counting and dimensions

Submission date: 3 January 2006, revised version 23 February 2006.


We prove a theorem comparing a well-behaved dimension notion to a second, more rudimentary dimension. Specialising to a non-standard counting measure, this generalizes a theorem of Larsen and Pink on an asymptotic upper bound for the intersection of a variety with a general finite subgroup of an algebraic group. As a second application we apply this to bad fields of positive characteristic, to give an asymptotic estimate for the number of Fq-rational points of a definable multiplicative subgroup similar to the Lang-Weil estimate for curves over finite fields.

Mathematics Subject Classification: 03C45

Keywords and phrases: dimension, counting, measure, asymptotic bounds

Full text: pdf, dvi, ps. (Old version: pdf, dvi, ps.)

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