Integral canonical models for Spin Shimura varieties

By Keerthi Madapusi Pera. Compositio Mathematica, 2012

85 citations recorded by the source corpus.

We construct regular integral canonical models for Shimura varieties attached to Spin and orthogonal groups at (possibly ramified) primes $p>2$ where the level is not divisible by $p$. We exhibit these models as schemes of ‘relative PEL type’ over integral canonical models of larger Spin Shimura varieties with good reduction at $p$. Work of Vasiu–Zink then shows that the classical Kuga–Satake construction extends over the integral models and that the integral models we construct are canonical in a very precise sense. Our results have applications to the Tate conjecture for K3 surfaces, as well as to Kudla’s program of relating intersection numbers of special cycles on orthogonal Shimura varieties to Fourier coefficients of modular forms.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bf6d0a400216c512caf6336538962b68725380e5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Faltings heights of abelian varieties with complex multiplication (2015, methodology): “ lattice. As in the introduction, the discriminant of Lis DL= [L∨ ∶ L]. 4.1. The GSpin Shimura variety. Let C(V) be the Cliﬀord algebra of (V,Q), with its Z~2Z-grading C(V) = C+(V)⊕C−(V). Recall from [Mada] that the spinor similitude group G= GSpin(V) is the algebraic group over Qwith G(R) = ™g∈ C+(”
Ekedahl-Oort Strata for Good Reductions of Shimura Varieties of Hodge Type (2013, background): “ieties of Hodge type but not necessarily of PEL type. E-O FOR SHV OF HODGE TYPE 25 4.1. CSpin-Shimura varieties. We explain what are CSpin-Shimura varieties and there integral canonical models follow [16]. Let Vbe a n+2-dimensionalQ-vectorspace with a quadratic form Qof signature (n,2). We will alwa”