The Fixed Point Locus of the Verschiebung on $mathcal{M}_X(2, 0)$ for Genus-2 Curves $X$ in Charateristic $2$

Canadian mathematical bulletin

YanHong Yang¹ 

[1] Department of Mathematics, Columbia University, New York, NY 10027, USA

关键词: vector bundle;    Frobenius pullback;    representation;    etale fundamental group;   

DOI  :  10.4153/CMB-2013-019-1

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We prove that for every ordinary genus-$2$ curve $X$ over a finitefield $kappa$ of characteristic $2$ with$extrm{Aut}(X/kappa)=mathbb{Z}/2mathbb{Z} imes S_3$, there exist$extrm{SL}(2,kappa[![s]!])$-representations of $pi_1(X)$ suchthat the image of $pi_1(overline{X})$ is infinite. This resultproduces a family of examples similar to Laszlo's counterexample to de Jong's question regarding the finiteness of the geometricmonodromy of representations of the fundamental group.

【 授权许可】

Unknown