1 results
The Fixed Point Locus of the Verschiebung on ℳX(2, 0) for Genus-2 Curves X in Charateristic 2
-
- Journal:
- Canadian Mathematical Bulletin / Volume 57 / Issue 2 / 14 June 2014
- Published online by Cambridge University Press:
- 20 November 2018, pp. 439-448
- Print publication:
- 14 June 2014
-
- Article
-
- You have access
- Export citation
-
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.
