Congruence Relations for Shimura Varieties Associated with GU(n–1, 1)

Koskivirta, Jean-Stefan

Canadian journal of mathematics, Tome 66 (2014) no. 6, pp. 1305-1326

Résumé

We prove the congruence relation for the $\bmod -p$ reduction of Shimura varieties associated with 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. Bültel, 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 $p-I\text{sog}$ is annihilated by a degree one polynomial in the Frobenius element $F$ , which implies the congruence relation.

Détail

DOI : 10.4153/CJM-2013-037-8

Mots-clés : 11G18, 14G35, 14K10, Shimura varieties, congruence relation

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