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arXiv · 1703.08281

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

Raymond Heitmann·Linquan Ma
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Abstract

We prove a version of weakly functorial big Cohen-Macaulay algebras that suffices to establish Hochster-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 pseudo-rational in mixed characteristic. Our proof uses perfectoid spaces and is inspired by the recent breakthroughs on the direct summand conjecture by André and Bhatt.

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Raymond Heitmann, Linquan Ma. 2018-03-18. Big Cohen-Macaulay algebras and the vanishing conjecture for maps of Tor in mixed characteristic. https://doi.org/10.2140/ant.2018.12.1659

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