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arXiv · 1611.09425

Horizontal Distribution Relations for Special Cycles on Unitary Shimura Varieties: Split Case

Reda Boumasmoud·Ernest Hunter Brooks·Dimitar Jetchev
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Abstract

We study the local behavior of special cycles on Shimura varieties for $\mathbf{U}(2, 1) \times \mathbf{U}(1, 1)$ in the setting of the Gan-Gross-Prasad conjectures at primes $\tau$ of the totally real field of definition of the unitary spaces which are split in the corresponding totally imaginary quadratic extension. We establish a local formula for their fields of definition, and prove a distribution relation between the Galois and Hecke actions on them. This complements work of \cite{jetchev:unitary} at inert primes, where the combinatorics of the formulas are reduced to calculations on the Bruhat--Tits trees, which in the split case must be replaced with higher-dimensional buildings.

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Reda Boumasmoud, Ernest Hunter Brooks, Dimitar Jetchev. 2016-11-28. Horizontal Distribution Relations for Special Cycles on Unitary Shimura Varieties: Split Case. https://arxiv.org/abs/1611.09425

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