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

  • STEVE MEAGHER (a1)

Abstract

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.

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[1] Chavdarov, N., ‘The generic irreducibility of the numerator of the zeta function in a family of curves with large monodromy’, Duke Math. J. 87 (1997), 151180.
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[4] Kosters, M., ‘A short proof of the Chebotarev density theorem for function fields’, Math. Commun. 22 (2017), 17.
[5] Kowalski, E., The Large Sieve and its Applications: Arithmetic Geometry, Random Walks and Discrete Groups (Cambridge University Press, Cambridge, 2008).
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[13]The Stacks Project, http://stacks.math.columbia.edu, 2017.
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A SIMPLE PROOF OF CHEBOTAREV’S DENSITY THEOREM OVER FINITE FIELDS

  • STEVE MEAGHER (a1)

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