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arXiv · 1509.01192

Minimal $F$-crystals and isomorphism numbers of isosimple $F$-crystals

Xiao Xiao
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Abstract

In this paper we generalize minimal $p$-divisible groups defined by Oort to $F$-crystal over an algebraically closed field of positive characteristic. We prove a structural theorem and give an explicit formula of the Frobenius endomorphism of the isosimple minimal $F$-crystals that are the building blocks of minimal $F$-crystals. We then define an invariant called the minimal height for $F$-crystals using minimal $F$-crystals and give an upper bound of the isomorphism numbers of isosimple $F$-crystals in terms of their ranks, Hodge slopes and Newton slopes.

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Xiao Xiao. 2015-09-03. Minimal $F$-crystals and isomorphism numbers of isosimple $F$-crystals. https://arxiv.org/abs/1509.01192

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