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arXiv · 2603.20548

Superrigidity for representations of transverse measured groupoids

Filippo Sarti·Alessio Savini
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Abstract

For $i=1,\ldots,k$, let $\mathbf{G}_i$ be a connected, simply connected, semisimple algebraic group over some local field $\kappa_i$ of characteristic zero. Let $G_i=\mathbf{G}_i(\kappa_i)$ be the $\kappa_i$-points of $\mathbf{G}_i$ and denote by $G=\prod_{i=1}^k G_i$. If we assume that $G$ has higher rank and each factor has positive rank, given an ergodic transverse $G$-system $(X,\mu,Y)$, we prove a superrigidity phenomenon for Zariski dense representations of the transverse groupoid $(G \ltimes X)|_Y$ into either an almost simple or a reductive algebraic group.

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Filippo Sarti, Alessio Savini. 2026-03-20. Superrigidity for representations of transverse measured groupoids. https://arxiv.org/abs/2603.20548

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