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arXiv · 2010.15160

On $BT_1$ group schemes and Fermat Jacobians

Rachel Pries·Douglas Ulmer
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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. We compare three classifications of $BT_1$ group schemes, due in large part to Kraft, Ekedahl, and Oort, and defined using words, canonical filtrations, and permutations. Using this comparison, we determine the Ekedahl--Oort types of Fermat quotient curves and we compute four invariants of the $p$-torsion group schemes of these curves.

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Rachel Pries, Douglas Ulmer. 2020-10-28. On $BT_1$ group schemes and Fermat Jacobians. https://arxiv.org/abs/2010.15160

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