The Étale locus in complete local rings

Pub Date : 2021-01-01 DOI:10.1090/conm/773/15532

R. Heitmann

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引用次数: 1

Abstract

Let R R be a complete local ring and let Q Q be a prime ideal of R R . It is determined precisely which conditions on R R are equivalent to the existence of a complete unramified regular local ring A A and an element g ∈ A − Q g\in A-Q such that R R is a finite A A -module and A g ⟶ R g A_g\longrightarrow R_g is étale . A number of other properties of the possible embeddings A ⟶ R A\longrightarrow R are developed in the process including the determination of precisely which fields can be coefficient fields in the Cohen-Gabber Theorem.

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完全局部环中的Étale轨迹

设R R是一个完全局部环，Q Q是R R的素理想。精确地确定了在R R上哪些条件等价于存在一个完全的非发散正则局部环a a和a -Q中的一个元素g∈a−Q g\，使得R R是一个有限的a a -模，并且a g R R_g。在此过程中发展了可能嵌入A × R的许多其他性质，包括确定Cohen-Gabber定理中哪些场可以是系数场。

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