# Non-ordinary curves with a Prym variety of low $p$-rank

@article{Celik2017NonordinaryCW,
title={Non-ordinary curves with a Prym variety of low \$p\$-rank},
author={Turku Ozlum Celik and Yara Elias and Burcin Gunes and Rachel Newton and Ekin Ozman and Rachel J. Pries and Lara Thomas},
journal={arXiv: Number Theory},
year={2017}
}
If $\pi: Y \to X$ is an unramified double cover of a smooth curve of genus $g$, then the Prym variety $P_\pi$ is a principally polarized abelian variety of dimension $g-1$. When $X$ is defined over an algebraically closed field $k$ of characteristic $p$, it is not known in general which $p$-ranks can occur for $P_\pi$ under restrictions on the $p$-rank of $X$. In this paper, when $X$ is a non-hyperelliptic curve of genus $g=3$, we analyze the relationship between the Hasse-Witt matrices of $X… Expand 1 Citations #### Figures from this paper Computing representation matrices for the action of Frobenius to cohomology groups An algorithm to compute the matrices for arbitrary algebraic varieties with defining equations over perfect fields of positive characteristic is given, and a specific efficient method is proposed, which works for complete intersections. Expand #### References SHOWING 1-10 OF 24 REFERENCES Ordinary and almost ordinary Prym varieties • Mathematics • Asian Journal of Mathematics • 2019 We study the relationship between the$p$-rank of a curve and the$p$-ranks of the Prym varieties of its cyclic covers in characteristic$p >0$. For arbitrary$p$,$g \geq 3$and$0 \leq f \leq g$,Expand Superspecial curves of genus 4 in small characteristic • Mathematics, Computer Science • Finite Fields Their Appl. • 2017 It is proved that there does not exist a superspecial curve of genus$4$in characteristic$7$, which implies the non-existence of maximal curves of genus$4$over$\mathbb{F}_{49}$, which updates the table at {\tt this http URL}. Expand Syzygies of torsion bundles and the geometry of the level ℓ modular variety over$\overline{\mathcal{M}}_{g}\$
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