正规和不可约Adic空间、有限态射的开性和Stein分解
Normal and Irreducible Adic Spaces, the Openness of Finite Morphisms and a Stein Factorization
摘要：
我们把刚性解析空间的几个基本几何性质转移到adic空间的世界中，更确切地说，转移到非阿基米德域上局部（弱）有限型的adic空间范畴中。这包括正规性，不可约性（特别是不可约分量）和斯坦分解定理。最值得注意的是，我们表明，有限态射的进空间是开放的基础和目标空间的温和的假设。
英文摘要：
We transfer several elementary geometric properties of rigid-analytic spaces to the world of adic spaces, more precisely to the category of adic spaces which are locally of (weakly) finite type over a non-archimedean field. This includes normality, irreducibility (in particular irreducible components) and a Stein factorization theorem. Most notably we show that finite morphisms of adic spaces are open under mild assumptions on the base and target space.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
