The Supersingular Locus of the Shimura Variety for GU(1, s)
Canadian journal of mathematics, Tome 62 (2010) no. 3, pp. 668-720
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In this paper we study the supersingular locus of the reduction modulo $p$ of the Shimura variety for $\text{GU}\left( 1,\,s \right)$ 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 $\text{GU}\left( 1,\,2 \right)$ , 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.
Vollaard, Inken. The Supersingular Locus of the Shimura Variety for GU(1, s). Canadian journal of mathematics, Tome 62 (2010) no. 3, pp. 668-720. doi: 10.4153/CJM-2010-031-2
@article{10_4153_CJM_2010_031_2,
author = {Vollaard, Inken},
title = {The {Supersingular} {Locus} of the {Shimura} {Variety} for {GU(1,} s)},
journal = {Canadian journal of mathematics},
pages = {668--720},
year = {2010},
volume = {62},
number = {3},
doi = {10.4153/CJM-2010-031-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-031-2/}
}
TY - JOUR AU - Vollaard, Inken TI - The Supersingular Locus of the Shimura Variety for GU(1, s) JO - Canadian journal of mathematics PY - 2010 SP - 668 EP - 720 VL - 62 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-031-2/ DO - 10.4153/CJM-2010-031-2 ID - 10_4153_CJM_2010_031_2 ER -
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