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Toroidal compactifications of integral m...
Pera, Keerthi Madapu...

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Toroidal compactifications of integral models of Shimura varieties of Hodge type by Pera, Keerthi Madapusi ( Author )
Lemonjar Open Access
Australian National University
27-07-2023
We construct projective toroidal compactifications for integral models of Shimura varieties of Hodge type. We also construct integral models of the minimal (Satake-Baily-Borel) compactification. Our results essentially reduce the problem to understanding the integral models themselves. As such, they cover all previously known cases of PEL type, as well as all cases of Hodge type involving parahoric level structures. At primes where the level is hyperspecial, we show that our compactifications are canonical in a precise sense. We also provide a new proof of Y. Morita's conjecture on the everywhere good reduction of abelian varieties whose Mumford-Tate group is anisotropic modulo center. Along the way, we demonstrate an interesting rationality property of Hodge cycles on abelian varieties with respect to p-adic analytic uniformizations.
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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1211.1731
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