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Perfectoid pure singularities
Bhargav Bhatt, Linquan Ma, Zsolt Patakfalvi +4
Fix a prime number . Inspired by the notion of -pure or -split singularities, we study the condition that a Noetherian ring with in its Jacobson radical is pure inside…
Test ideals in mixed characteristic: a unified theory up to perturbation
Bhargav Bhatt, Linquan Ma, Zsolt Patakfalvi +5
Let be an integral scheme of finite type over a complete DVR of mixed characteristic. We provide a definition of a test ideal which agrees with the multiplier ideal after inver…
Crystals and Chern classes
Bhargav Bhatt
The goal of this paper is to study the Chern classes of coherent sheaves (and more generally perfect complexes) that admit crystal structures in the setting of crystalline cohomolo…
Perfectoid spaces
Peter Scholze
We introduce a certain class of so-called perfectoid rings and spaces, which give a natural framework for Faltings' almost purity theorem, and for which there is a natural tilting…