DOI: 10.1017/s1474748026102187 ISSN: 1474-7480

THE BASIC LOCUS OF THE UNITARY SHIMURA VARIETY WITH MINUSCULE PARAHORIC LEVEL STRUCTURE, AND SPECIAL CYCLES

Sungyoon Cho
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Abstract

In this paper, we study the basic locus in the fibre at p of a certain unitary Shimura variety with a certain parahoric level structure. The basic locus

M s s ^ $\widehat {{\mathcal M}^{ss}}$ ModifyingAbove script upper M Superscript s s Baseline With caret
is uniformized by a formal scheme
N ${\mathcal N}$ script upper N
, which is called the Rapoport–Zink space. We show that the irreducible components of the induced reduced subscheme
N r e d ${\mathcal N}_{red}$ script upper N Subscript r e d
of
N ${\mathcal N}$ script upper N
are Deligne–Lusztig varieties and their intersection behaviour is controlled by a certain Bruhat-Tits building. Also, we define special cycles in
N ${\mathcal N}$ script upper N
and study their intersection multiplicities.

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