论文标题
关于与投影措施不变领域的排名一号共生的琐碎性
On the trivializability of rank-one cocycles with an invariant field of projective measures
论文作者
论文摘要
令$ g $为$ \ text {so}^\ circ（n，1）$ for $ n \ geq 3 $，并考虑一个晶格$γ<g $。给定标准的Borel概率$γ$ -Space $（ω，μ）$，考虑可测量的Cocycle $σ：γ\ Timesω\ rightarrow \ Mathbf {H}（H}（H}（κ）$，其中$ \ MATHBF {H} $是一个连接的Elgebraic $κ$κ$κ$ - $ - $ - $ - $ - $ - $ - $ $ $κ$κ。在假设$ g $和一对$（\ mathbf {h}，κ）$之间的兼容性下，我们表明，如果$σ$在合适的投影空间上接受了概率度量的等效领域，则$σ$是可琐的。 在复杂的双曲线病例中，类似的结果成立。
Let $G$ be $\text{SO}^\circ(n,1)$ for $n \geq 3$ and consider a lattice $Γ< G$. Given a standard Borel probability $Γ$-space $(Ω,μ)$, consider a measurable cocycle $σ:Γ\times Ω\rightarrow \mathbf{H}(κ)$, where $\mathbf{H}$ is a connected algebraic $κ$-group over a local field $κ$. Under the assumption of compatibility between $G$ and the pair $(\mathbf{H},κ)$, we show that if $σ$ admits an equivariant field of probability measures on a suitable projective space, then $σ$ is trivializable. An analogous result holds in the complex hyperbolic case.
