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

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Abstract

For a projective curve C⊂Pn defined over a finite field Fq we study the statistics of the Fq-structure of a section of C by a random hyperplane defined over Fq in the q→∞ 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.

Original languageEnglish
Article numberrnz120
Number of pages33
JournalInternational Mathematics Research Notices
DOIs
StatePublished - 5 Jul 2019

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