论文标题
典型的纯刚性分析品种的当地恒定
Uniform local constancy of étale cohomology of rigid analytic varieties
论文作者
论文摘要
我们证明了一些$ \ ell $独立的结果，这些结果是对刚性分析品种的典型构成共同体的局部构成结果。结果，我们表明，在代数封闭的完整非架构的非架构的非架构中，适当的方案的封闭式将在分析拓扑中有一个很小的开放社区，以便，对于每个质数$ \ ell $ $ \ ell $都不同，与残留的特征不同，封闭的亚cheme和开放社区具有$ \ mathbb z/\ el \ el \ mathbb z $ \ mathbb z $ - c $ - combb z $ - c $ - comcect。 Huber证明了每个$ \ ell $的公开社区的存在。证明中的一个关键成分是统一的Orgogozo定理对附近周期的兼容性在一般基础上随着基础变化而在一般基础上的兼容性。
We prove some $\ell$-independence results on local constancy of étale cohomology of rigid analytic varieties. As a result, we show that a closed subscheme of a proper scheme over an algebraically closed complete non-archimedean field has a small open neighborhood in the analytic topology such that, for every prime number $\ell$ different from the residue characteristic, the closed subscheme and the open neighborhood have the same étale cohomology with $\mathbb Z/\ell \mathbb Z$-coefficients. The existence of such an open neighborhood for each $\ell$ was proved by Huber. A key ingredient in the proof is a uniform refinement of a theorem of Orgogozo on the compatibility of the nearby cycles over general bases with base change.
