A survey of the Torelli locus and Newton polygons that corrects a previously erroneous genus computation and thereby proves new infinite families of supersingular curves of genus δp(p−1)/2.
$p$-torsion for unramified Artin--Schreier covers of curves
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abstract
Let $Y\to X$ be an unramified Galois cover of curves over a perfect field $k$ of characteristic $p>0$ with $\mathrm{Gal}(Y/X)\cong\mathbb{Z}/p\mathbb{Z}$, and let $J_X$ and $J_Y$ be the Jacobians of $X$ and $Y$ respectively. We consider the $p$-torsion subgroup schemes $J_X[p]$ and $J_Y[p]$, analyze the Galois-module structure of $J_Y[p]$, and find restrictions this structure imposes on $J_Y[p]$ (for example, as manifested in its Ekedahl--Oort type) taking $J_X[p]$ as given.
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The Torelli locus and Newton polygons
A survey of the Torelli locus and Newton polygons that corrects a previously erroneous genus computation and thereby proves new infinite families of supersingular curves of genus δp(p−1)/2.