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

Yang, YanHong

Canadian mathematical bulletin, Tome 57 (2014) no. 2, pp. 439-448

Résumé

We prove that for every ordinary genus-2 curve $X$ over a finite field $\kappa$ of characteristic 2 with $\text{Aut}\left( X/\kappa\right)\,=\,\mathbb{Z}/2\mathbb{Z}\,\times \,{{S}_{3}}$ there exist $\text{SL}\left( 2,\,\kappa \left[\!\left[ s \right]\!\right] \right)$ -representations of ${{\pi }_{1}}\left( X \right)$ such that the image of ${{\pi }_{1}}\left( \overline{X} \right)$ is infinite. This result produces a family of examples similar to Y. Laszlo’s counterexample to A. J. de Jong’s question regarding the finiteness of the geometric monodromy of representations of the fundamental group.

Détail

DOI : 10.4153/CMB-2013-019-1

Mots-clés : 14H60, 14D05, 14G15, vector bundle, Frobenius pullback, representation, etale fundamental group

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