| Autor: |
Drimbe, Daniel, Ioana, Adrian, Peterson, Jesse |
| Rok vydání: |
2019 |
| Předmět: |
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| Zdroj: |
Duke Math. J. 157, no. 2 (2011), 337-367 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1215/00127094-2011-008 |
| Popis: |
Let $\Gamma$ be an irreducible lattice in a product of two locally compact groups and assume that $\Gamma$ is densely embedded in a profinite group $K$. We give necessary conditions which imply that the left translation action $\Gamma\curvearrowright K$ is "virtually" cocycle superrigid: any cocycle $w:\Gamma\times K\rightarrow\Delta$ with values in a countable group $\Delta$ is cohomologous to a cocycle which factors through the map $\Gamma\times K\rightarrow\Gamma\times K_0$, for some finite quotient group $K_0$ of $K$. As a corollary, we deduce that any ergodic profinite action of $\Gamma=\text{SL}_2(\mathbb Z[S^{-1}])$ is virtually cocycle superrigid and virtually W$^*$-superrigid, for any finite nonempty set of primes $S$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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