6 papers
Local cohomology modules with nonclosed support
Bhargav Bhatt, Linquan Ma
We construct noetherian rings admitting local cohomology modules with nonclosed support, or equivalently with infinitely many minimal primes; this answers a question of Huneke--Lyu…
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…
Lim Cohen-Macaulay sequences of modules
Bhargav Bhatt, Mel Hochster, Linquan Ma
We introduce the notion of a lim Cohen-Macaulay sequence of modules. We prove the existence of such sequences in positive characteristic, and show that their existence in mixed cha…
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…