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7 papers
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…
-finite schemes have a dualizing complex
Bhargav Bhatt, Manuel Blickle, Karl Schwede +1
In this paper we show that any Noetherian -finite scheme has a dualizing complex with the property that for all finite type maps between $F…
Plus-pure thresholds of some cusp-like singularities in mixed characteristic
Hanlin Cai, Suchitra Pande, Eamon Quinlan-Gallego +2
Log-canonical and -pure thresholds of pairs in equal characteristic admit an analog in the recent theory of singularities in mixed characteristic, which is known as the plus-pur…
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…
Perfectoid signature, perfectoid Hilbert-Kunz multiplicity, and an application to local fundamental groups
Hanlin Cai, Seungsu Lee, Linquan Ma +2
We define a (perfectoid) mixed characteristic version of -signature and Hilbert-Kunz multiplicity by utilizing the perfectoidization functor of Bhatt-Scholze and Faltings' norma…
Mittag-Leffler modules and variants on intersection flatness
Rankeya Datta, Neil Epstein, Kevin Tucker
We systematically study the intersection flatness and Ohm-Rush properties for modules over a commutative ring, drawing inspiration from the work of Ohm and Rush and of Hochster and…