Toroidal compactifications of integral models of Shimura varieties of Hodge type
By Keerthi Madapusi Pera. 2012
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We construct projective toroidal compactifications for integral models of Shimura varieties of Hodge type that parameterize isogenies of abelian varieties with additional structure. 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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/080831d1d2b406cdb4bc2bc83fc03f1cb328c46f
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Cycles on Shimura varieties via geometric Satake (2017, background): “On the other hand, the Hecke algebra Cc(G(Zp)\G(Qp)/G(Zp)) naturally acts on Hc(Shμ,k̄v): the existence of smooth toroidal compactification ([Lan13] [MP15]) implies that after choosing a specialization map k̄v → Ēv, there is an isomorphism Hc(Shμ,k̄v) ' Hc(ShK(G,X)Ēv), and since the action of the He”