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For an arbitrary discrete probability-measure-preserving groupoid $G$, weprovide a characterization of property (T) for $G$ in terms of the groupoid vonNeumann algebra $L(G)$. More generally, we obtain a characterization ofrelative property (T) for a subgroupoid $H\subset G$ in terms of the inclusion$L\left( H\right) \subset L\left( G\right) $.

A von Neumann algebra characterization of property (T) for groupoids