Finite étale extensions of Tate rings and decompletion of perfectoid algebras

Autor:	Kazuma Shimomoto, Kei Nakazato
Rok vydání:	2022
Předmět:	Pure mathematics Ring (mathematics) Algebra and Number Theory Mathematics::Commutative Algebra Completeness (order theory) Perfectoid Trace map Extension (predicate logic) Base (topology) Mathematics Descent (mathematics)
Zdroj:	Journal of Algebra. 589:114-158
ISSN:	0021-8693
DOI:	10.1016/j.jalgebra.2021.09.018
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::42b3faba3c7aa89c6b2b2c3d20997f66 https://doi.org/10.1016/j.jalgebra.2021.09.018 Zobrazit plný text záznamu Full Text from ScienceDirect