Canonical sections of the Hodge bundle over Ekedahl-Oort strata of Shimura varieties of Hodge type

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• 作者：Jean-Stefan Koskivirta ^{jeanstefan.koskivirta@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Abelian varieties ; Hasse invariant ; Shimura varieties ; Ekedahl&ndash ; Oort stratification ; Hodge bundle
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：1 March 2016
• 年：2016
• 卷：449
• 期：Complete
• 页码：446-459
• 全文大小：360 K

文摘

We construct canonical non-vanishing global sections of powers of the Hodge bundle on each Ekedahl–Oort stratum of a Hodge type Shimura variety. In particular we recover the quasi-affineness of the Ekedahl–Oort strata. In the projective case, this gives a very short proof of non-emptiness of Ekedahl–Oort strata. It follows that the Newton strata are also nonempty, by a result of S. Nie. From the canonicity of our construction, we deduce the fact that the μ-ordinary locus is determined by the Ekedahl–Oort strata of its image under any embedding of Shimura varieties.