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Mathematics > Number Theory

arXiv:1805.05454 (math)
[Submitted on 14 May 2018 (v1), last revised 31 Mar 2019 (this version, v3)]

Title:Monodromy of Hyperplane Sections of Curves and Decomposition Statistics over Finite Fields

Authors:Alexei Entin
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Abstract:For a projective curve $C\subset\mathbf{P}^n$ defined over $\mathbf{F}_q$ we study the statistics of the $\mathbf{F}_q$-structure of a section of $C$ by a random hyperplane defined over $\mathbf{F}_q$ in the $q\to\infty$ limit. We obtain a very general equidistribution result for this problem. We deduce many old and new results about decomposition statistics over finite fields in this limit. Our main tool will be the calculation of the monodromy of transversal hyperplane sections of a projective curve.
Subjects: Number Theory (math.NT)
Cite as: arXiv:1805.05454 [math.NT]
  (or arXiv:1805.05454v3 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1805.05454

Submission history

From: Alexei Entin [view email]
[v1] Mon, 14 May 2018 21:27:54 UTC (24 KB)
[v2] Mon, 20 Aug 2018 13:30:37 UTC (24 KB)
[v3] Sun, 31 Mar 2019 13:27:00 UTC (25 KB)
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