论文标题
泰特戒指的有限étale扩展和完美代数的重新完成
Finite étale extension of Tate rings and decompletion of perfectoid algebras
论文作者
论文摘要
在本文中，我们使用痕量图研究了在某些环扩展下的理想分离和完整性的行为。然后，我们证明，在合理条件下，基本环的ADIC完整性是遗传性的。我们的目标是在完成的某些环理论特性的上升和下降中给出许多结果。作为应用程序，我们将概念细节提供给戴维斯和吉德拉的几乎纯度定理的证明。 witt完美的环的优势是，人们不需要假设环是完整的和分开的。
In this paper, we examine the behavior of ideal-adic separatedness and completeness under certain ring extensions using trace map. Then we prove that adic completeness of a base ring is hereditary to its ring extension under reasonable conditions. We aim to give many results on ascent and descent of certain ring theoretic properties under completion. As an application, we give conceptual details to the proof of the almost purity theorem for Witt-perfect rings by Davis and Kedlaya. Witt-perfect rings have the advantage that one does not need to assume that the rings are complete and separated.
