The Fixed Point Locus of the Verschiebung on M_x(2,0) for Genus-2 Curves X in Charateristic 2

2011/11/25 by Yanhong Yang, Yang, Yanhong · 1 citation
Computer Science · Mathematics · #14D05 #14G15 #14H60 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1111.5887

openalex publication_date 2011/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we prove that for every ordinary genus-2 curve X over a finite field κ of characteristic 2 with Aut(X/κ)=\dbZ/2\dbZ × S₃, there exist SL(2,κ\sembracks)-representations of π₁(X) such that the image of π₁(X) is infinite. This result gives a geometric interpretation of Laszlo's counterexample [12] to a question regarding the finiteness of the geometric monodromy of representations of the fundamental group [4].

Cited by

• Explicit computation of the generic degree of the generalized Verschiebung in rank two

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