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A SIMPLE PROOF OF CHEBOTAREV’S DENSITY THEOREM OVER FINITE FIELDS

Part of: Arithmetic problems. Diophantine geometry Arithmetic algebraic geometry

Published online by Cambridge University Press:  12 July 2018

STEVE MEAGHER Open the ORCID record for STEVE MEAGHER [Opens in a new window]
STEVE MEAGHER*
Affiliation:
School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia email [email protected]
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Abstract

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We present a simple proof of the Chebotarev density theorem for finite morphisms of quasi-projective varieties over finite fields following an idea of Fried and Kosters for function fields. The key idea is to interpret the number of rational points with a given Frobenius conjugacy class as the number of rational points of a twisted variety, which is then bounded by the Lang–Weil estimates.

Keywords

Chebotarev density theoremquasi-projective varietyFrobenius conjugacy classLang–Weil bounds

MSC classification

Primary: 11G25: Varieties over finite and local fields
Secondary: 14G15: Finite ground fields
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 2 , October 2018 , pp. 196 - 202
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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