Big Cohen-Macaulay algebras and the vanishing conjecture for maps of Tor in mixed characteristic

被引：19

作者：

Heitmann, Raymond ^{[1
]}

Ma, Linquan ^{[2
]}

机构：

[1] Univ Texas Austin, Austin, TX 78712 USA

[2] Purdue Univ, W Lafayette, IN 47907 USA

来源：

ALGEBRA & NUMBER THEORY | 2018年 / 12卷 / 07期

关键词：

big Cohen-Macaulay algebras; direct summand conjecture; perfectoid space; vanishing conjecture for maps of Tor; pseudorational singularities; DIRECT SUMMAND CONJECTURE;

D O I：

10.2140/ant.2018.12.1659

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a version of weakly functorial big Cohen-Macaulay algebras that suffices to establish Hochster and Huneke's vanishing conjecture for maps of Tor in mixed characteristic. As a corollary, we prove an analog of Boutot's theorem that direct summands of regular rings are pseudorational in mixed characteristic. Our proof uses perfectoid spaces and is inspired by the recent breakthroughs on the direct summand conjecture by Andre and Bhatt.

引用

页码：1659 / 1674

页数：16

共 18 条

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[16] Perfectoid Spaces
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[J]. PUBLICATIONS MATHEMATIQUES DE L IHES, 2012, (116): : 245 - 313
[17] [No title captured]
[18] [No title captured]

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