## Abstract

Let p be a prime number and let k be an algebraically closed field of characteristic p. A BT_{1} group scheme over k is a finite commutative group scheme which arises as the kernel of p on a p-divisible (Barsotti–Tate) group. Our main result is that every BT_{1} group scheme over k occurs as a direct factor of the p-torsion group scheme of the Jacobian of an explicit curve defined over F_{p}. We also treat a variant with polarizations. Our main tools are the Kraft classification of BT_{1} group schemes, a theorem of Oda, and a combinatorial description of the de Rham cohomology of Fermat curves.

Original language | English (US) |
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Pages (from-to) | 525-537 |

Number of pages | 13 |

Journal | Proceedings of the American Mathematical Society |

Volume | 150 |

Issue number | 2 |

DOIs | |

State | Published - 2022 |

Externally published | Yes |

## Keywords

- Abelian variety
- Curve
- De Rham cohomology
- Dieudonné module
- Fermat curve
- Finite field
- Frobenius
- Group scheme
- Jacobian
- P-divisible group
- Verschiebung

## ASJC Scopus subject areas

- General Mathematics
- Applied Mathematics

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