On the number of cusps of orthogonal Shimura varieties
Tóm tắt
We study the cusps of Shimura varieties arising from indefinite lattices splitting two hyperbolic planes. We determine the number of 0-dimensional cusps for a given variety and, when the lattice is maximal, we relate the genus of the lattice to the number of
$$1$$
-dimensional cusps and determine an explicit formula. As every lattice is contained as a sublattice of finite index in a maximal lattice, the results we obtain are useful in a general analysis.
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