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A dimension formula for Ekedahl-Oort strata

Ben Moonen (2004)

Annales de l’institut Fourier

We study the Ekedahl-Oort stratification on moduli spaces of PEL type. The strata are indexed by the classes in a Weyl group modulo a subgroup, and each class has a distinguished representative of minimal length. The main result of this paper is that the dimension of a stratum equals the length of the corresponding Weyl group element. We also discuss some explicit examples.

An alternative description of the Drinfeld p -adic half-plane

Stephen Kudla, Michael Rapoport (2014)

Annales de l’institut Fourier

We show that the Deligne formal model of the Drinfeld p -adic half-plane relative to a local field F represents a moduli problem of polarized O F -modules with an action of the ring of integers in a quadratic extension E of F . The proof proceeds by establishing a comparison isomorphism with the Drinfeld moduli problem. This isomorphism reflects the accidental isomorphism of SL 2 ( F ) and SU ( C ) ( F ) for a two-dimensional split hermitian space C for E / F .

An effective result of André-Oort type II

Lars Kühne (2013)

Acta Arithmetica

We prove some new effective results of André-Oort type. In particular, we state certain uniform improvements of the main result in [L. Kühne, Ann. of Math. 176 (2012), 651-671]. We also show that the equation X + Y = 1 has no solution in singular moduli. As a by-product, we indicate a simple trick rendering André's proof of the André-Oort conjecture effective. A significantly new aspect is the usage of both the Siegel-Tatuzawa theorem and the weak effective lower bound on the class number of an...

Cohomology of the boundary of Siegel modular varieties of degree two, with applications

J. William Hoffman, Steven H. Weintraub (2003)

Fundamenta Mathematicae

Let 𝓐₂(n) = Γ₂(n)∖𝔖₂ be the quotient of Siegel's space of degree 2 by the principal congruence subgroup of level n in Sp(4,ℤ). This is the moduli space of principally polarized abelian surfaces with a level n structure. Let 𝓐₂(n)* denote the Igusa compactification of this space, and ∂𝓐₂(n)* = 𝓐₂(n)* - 𝓐₂(n) its "boundary". This is a divisor with normal crossings. The main result of this paper is the determination of H(∂𝓐₂(n)*) as a module over the finite group Γ₂(1)/Γ₂(n). As an application...

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