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Search: MSC category 14K10 ( Algebraic moduli, classification [See also 11G15] )

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1. CJM Online first

Koskivirta, Jean-Stefan
Congruence Relations for Shimura Varieties Associated with $GU(n-1,1)$
We prove the congruence relation for the mod-$p$ reduction of Shimura varieties associated to a unitary similitude group $GU(n-1,1)$ over $\mathbb{Q}$, when $p$ is inert and $n$ odd. The case when $n$ is even was obtained by T. Wedhorn and O. B?ltel, as a special case of a result of B. Moonen, when the $\mu$-ordinary locus of the $p$-isogeny space is dense. This condition fails in our case. We show that every supersingular irreducible component of the special fiber of $p\textrm{-}\mathscr{I}sog$ is annihilated by a degree one polynomial in the Frobenius element $F$, which implies the congruence relation.

Keywords:Shimura varieties, congruence relation
Categories:11G18, 14G35, 14K10

2. CJM 2010 (vol 62 pp. 668)

Vollaard, Inken
The Supersingular Locus of the Shimura Variety for GU(1,s)
In this paper we study the supersingular locus of the reduction modulo $p$ of the Shimura variety for $GU(1,s)$ in the case of an inert prime $p$. Using Dieudonné theory we define a stratification of the corresponding moduli space of $p$-divisible groups. We describe the incidence relation of this stratification in terms of the Bruhat--Tits building of a unitary group. In the case of $GU(1,2)$, we show that the supersingular locus is equidimensional of dimension 1 and is of complete intersection. We give an explicit description of the irreducible components and their intersection behaviour.

Categories:14G35, 11G18, 14K10

3. CJM 2003 (vol 55 pp. 839)

Lee, Min Ho
Cohomology of Complex Torus Bundles Associated to Cocycles
Equivariant holomorphic maps of Hermitian symmetric domains into Siegel upper half spaces can be used to construct families of abelian varieties parametrized by locally symmetric spaces, which can be regarded as complex torus bundles over the parameter spaces. We extend the construction of such torus bundles using 2-cocycles of discrete subgroups of the semisimple Lie groups associated to the given symmetric domains and investigate some of their properties. In particular, we determine their cohomology along the fibers.

Categories:14K10, 14D06, 14F99

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