The authors construct a canonical formal group action on μ-ordinary Igusa varieties for Hodge type Shimura data that integrates Maass-Shimura operators and, via p-adic Fourier theory, yields a unified algebra action encoding both p-adic differential operators and Hecke operators.
Independence of $\ell$ for Frobenius conjugacy classes attached to abelian varieties
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Let $A$ be an abelian variety over a number field $\mathrm E\subset \mathbb C$ and let $\mathbf G$ denote the Mumford--Tate group of $A$. After replacing $\mathrm E$ by a finite extension, the action of the absolute Galois group $\mathrm{Gal}(\overline{\mathrm E}/\mathrm E)$ on the $\ell$-adic cohomology $\mathrm{H}^1_{\mathrm{\acute{e}t}}(A_{\overline{\mathrm E}},\mathbb Q_\ell)$ factors through $\mathbf G(\mathbb Q_\ell).$ We show that for $v$ an odd prime of $\mathrm E$ where $A$ has good reduction, the conjugacy class of Frobenius $\mathrm{Frob}_v$ in $\mathbf G(\mathbb Q_\ell)$ is independent of $\ell$. Along the way we prove that every point in the $\mu$-ordinary locus of the special fiber of Shimura varieties has a special point lifting it.
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math.NT 3representative citing papers
Constructs functorial Igusa stacks for Hodge-type Shimura varieties, yielding a sheaf on Bun_G that controls cohomology and proves compatibility with the semisimple local Langlands correspondence of Fargues-Scholze while establishing torsion vanishing for proper cases.
Constructs integral models for Shimura varieties of abelian type with parahoric level at odd primes that are étale locally isomorphic to local models.
citing papers explorer
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$p$-adic Maass--Shimura operators on $\mu$-ordinary Igusa varieties
The authors construct a canonical formal group action on μ-ordinary Igusa varieties for Hodge type Shimura data that integrates Maass-Shimura operators and, via p-adic Fourier theory, yields a unified algebra action encoding both p-adic differential operators and Hecke operators.
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Igusa Stacks and the Cohomology of Shimura Varieties
Constructs functorial Igusa stacks for Hodge-type Shimura varieties, yielding a sheaf on Bun_G that controls cohomology and proves compatibility with the semisimple local Langlands correspondence of Fargues-Scholze while establishing torsion vanishing for proper cases.
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Integral models of Shimura varieties with parahoric level structure, II
Constructs integral models for Shimura varieties of abelian type with parahoric level at odd primes that are étale locally isomorphic to local models.