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

Published online by Cambridge University Press:  20 November 2018

YanHong Yang
YanHong Yang*
Affiliation:
Department of Mathematics, Columbia University, New York, NY 10027, USA e-mail: yhyang@math.columbia.edu
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Abstract.

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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.

Keywords

14H6014D0514G15vector bundleFrobenius pullbackrepresentationetale fundamental group
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 2 , 14 June 2014 , pp. 439 - 448
Copyright
Copyright © Canadian Mathematical Society 2014

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