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

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

2011-11-25

arxiv.org/abs/1111.5887v3

Mathematics

Algebraic Geometry

We replace the previous proof of Theorem 1.2 by a more geometric proof

Scientific paper

In this note, we prove that for every ordinary genus-2 curve $X$ over a finite field $\kappa$ of characteristic 2 with $\text{Aut}(X/\kappa)=\db{Z}/2\db{Z} \times S_3$, there exist $\text{SL}(2,\kappa\sembrack{s})$-representations of $\pi_1(X)$ such that the image of $\pi_1(\bar{X})$ 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].

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