Almost algebraic actions of algebraic groups and applications to algebraic representations

作者：Bader Uri^*; Duchesne Bruno; Lecureux Jean

来源：Groups, Geometry, and Dynamics, 2017, 11(2): 705-738.

DOI：10.4171/GGD/413

• Complete separable valued fields
• probability measures on algebraic varieties
• algebraic representations of amenable ergodic actions
• Margulis-Zimmer super-rigidity

Let G be an algebraic group over a complete separable valued field k. We discuss the dynamics of the G-action on spaces of probability measures on algebraic G-varieties. We show that the stabilizers of measures are almost algebraic and the orbits are separated by open invariant sets. We discuss various applications, including existence results for algebraic representations of amenable ergodic actions. The latter provides an essential technical step in the recent generalization of Margulis-Zimmer super-rigidity phenomenon [2].

• 出版日期2017