Geodesic
Cocycle superrigidity for profinite actions of irreducible lattices
Daniel Drimbe1 ; Adrian Ioana2 orcid ; Jesse Peterson3
1KU Leuven, Belgium
2Unuversity of California San Diego, La Jolla, USA
3Vanderbilt University, Nashville, USA
Groups, geometry, and dynamics, Tome 17 (2023) no. 1, pp. 315-329

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DOI

Let Γ be an irreducible lattice in a product of two locally compact groups and assume that Γ is densely embedded in a profinite group K. We give necessary conditions which imply that the left translation action Γ↷K is “virtually” cocycle superrigid: any cocycle w:Γ×K→Δ with values in a countable group Δ is cohomologous to a cocycle which factors through the map Γ×K→Γ×K0​ for some finite quotient group K0​ of K. As a corollary, we deduce that any ergodic profinite action of Γ=SL2​(Z[S−1]) is virtually cocycle superrigid and virtually W∗-superrigid for any finite nonempty set of primes S.
DOI : 10.4171/ggd/700
Classification : 37-XX, 46-XX
Mots-clés : Cocycle superrigidity, deformation/rigidity theory, orbit equivalence, profinite action, irreducible lattice, strong ergodicity

Daniel Drimbe  1   ; Adrian Ioana  2   ; Jesse Peterson  3

1 KU Leuven, Belgium
2 Unuversity of California San Diego, La Jolla, USA
3 Vanderbilt University, Nashville, USA 
Daniel Drimbe; Adrian Ioana; Jesse Peterson. Cocycle superrigidity for profinite actions of irreducible lattices. Groups, geometry, and dynamics, Tome 17 (2023) no. 1, pp. 315-329. doi: 10.4171/ggd/700
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     year = {2023},
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     number = {1},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/700/}
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