The Étale locus in complete local rings

IF 0.3 4区数学 Q4 MATHEMATICS

Journal of Commutative Algebra 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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来源期刊

Journal of Commutative Algebra MATHEMATICS-

CiteScore

0.80

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Commutative Algebra publishes significant results in the area of commutative algebra and closely related fields including algebraic number theory, algebraic geometry, representation theory, semigroups and monoids. The journal also publishes substantial expository/survey papers as well as conference proceedings. Any person interested in editing such a proceeding should contact one of the managing editors.