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Canonical Integral Models of Shimura Varieties of Abelian Type

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arxiv 2402.05727 v1 pith:LTOEV2FP submitted 2024-02-08 math.NT math.AG

Patrick Daniels , Alex Youcis This is my paper · ORCID
classification math.NTmath.AG
keywords shimuraabelianmodelstypevarietiescanonicalintegralchoices
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abstract

We prove a conjecture of Pappas and Rapoport for all Shimura varieties of abelian type with parahoric level structure when $p>3$ by showing that the Kisin-Pappas-Zhou integral models of Shimura varieties of abelian type are canonical. In particular, this shows that these models of are independent of the choices made during their construction, and that they satisfy functoriality with respect to morphisms of Shimura data.

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  1. Strongly compatible systems associated to semistable abelian varieties

    math.NT 2025-05 unverdicted novelty 8.0 of 10

    For an abelian variety over a number field with semistable reduction at v, the Mumford-Tate group valued Weil-Deligne representation at v is defined over Q and is independent of the auxiliary prime l.

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