From the 1 of 4 linked papers with an AI index.
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4 papers
Local cohomology modules with nonclosed support
Bhargav Bhatt, Linquan Ma
The authors construct Noetherian rings whose local cohomology modules have nonclosed support, i.e., infinitely many minimal primes, thereby answering a question of Huneke–Lyubeznik…
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…
Diophantine sets
Bhargav Bhatt, Bjorn Poonen
Diophantine subsets of play a key role in the negative answer to Hilbert's tenth problem. The definition of diophantine set generalizes in several ways to other commut…
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…