Cocycle superrigidity for profinite actions of irreducible lattices

  • Daniel Drimbe

    KU Leuven, Belgium
  • Adrian Ioana

    Unuversity of California San Diego, La Jolla, USA
  • Jesse Peterson

    Vanderbilt University, Nashville, USA
Cocycle superrigidity for profinite actions of irreducible lattices cover
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Abstract

Let be an irreducible lattice in a product of two locally compact groups and assume that is densely embedded in a profinite group . We give necessary conditions which imply that the left translation action is “virtually” cocycle superrigid: any cocycle with values in a countable group is cohomologous to a cocycle which factors through the map for some finite quotient group of . As a corollary, we deduce that any ergodic profinite action of is virtually cocycle superrigid and virtually W-superrigid for any finite nonempty set of primes .

Cite this article

Daniel Drimbe, Adrian Ioana, Jesse Peterson, Cocycle superrigidity for profinite actions of irreducible lattices. Groups Geom. Dyn. 17 (2023), no. 1, pp. 315–329

DOI 10.4171/GGD/700