17 citations · 48 across the 20 of their papers we have counts for
27 papers · 1 filter
On an ideal membership problem
Melvin Hochster, Jack Jeffries, Nawaj KC +1
Suppose are elements of a regular ring , where . The first author proved that ;…
The variety of nilpotent matrices is -regular
Jack Jeffries, Vaibhav Pandey, Anurag K. Singh
We give an elementary proof that the coordinate ring of the variety of nilpotent matrices is -regular; over an infinite field , this ring also arises as the nullcone for the…
Regularity is bounded on a quasi-excellent Noetherian scheme
Alessandro De Stefani, Jack Jeffries, Nawaj KC +1
A point of a scheme has an associated tangent cone, the spectrum of a standard graded algebra encoding the local singularity. Its homological complexity can be measured by its grad…
Local cohomology of modular invariant rings
Kriti Goel, Jack Jeffries, Anurag K. Singh
For a field, consider a finite subgroup of with its natural action on the polynomial ring . Let denote the homo…
When are the natural embeddings of classical invariant rings pure?
Melvin Hochster, Jack Jeffries, Vaibhav Pandey +1
Consider a reductive linear algebraic group acting linearly on a polynomial ring over an infinite field; key examples are the general linear group, the symplectic group, th…
Resolutions of differential operators of low order for an isolated hypersurface singularity
Rachel N. Diethorn, Jack Jeffries, Claudia Miller +4
In this paper we develop a new approach for studying differential operators of an isolated singularity graded hypersurface ring defining a surface in affine three-space over a…
Bernstein-Sato theory for singular rings in positive characteristic
Jack Jeffries, Luis Núñez-Betancourt, Eamon Quinlan-Gallego
The Bernstein-Sato polynomial is an important invariant of an element or an ideal in a polynomial ring or power series ring of characteristic zero, with interesting connections to…
Bernstein-Sato polynomials in commutative algebra
Josep Àlvarez Montaner, Jack Jeffries, Luis Núñez-Betancourt
This is an expository survey on the theory of Bernstein-Sato polynomials with special emphasis in its recent developments and its importance in commutative algebra.
A Jacobian criterion for nonsingularity in mixed characteristic
Melvin Hochster, Jack Jeffries
We give a version of the usual Jacobian characterization of the defining ideal of the singular locus in the equal characteristic case: the new theorem is valid for essentially affi…
A uniform Chevalley theorem for direct summands of polynomial rings in mixed characteristic
Alessandro De Stefani, Eloísa Grifo, Jack Jeffries
We prove an explicit uniform Chevalley theorem for direct summands of graded polynomial rings in mixed characteristic. Our strategy relies on the introduction of a new type of diff…
Bernstein's inequality and holonomicity for certain singular rings
Josep Àlvarez Montaner, Daniel J. Hernández, Jack Jeffries +3
In this manuscript we prove the Bernstein inequality and develop the theory of holonomic D-modules for rings of invariants of finite groups in characteristic zero, and for strongly…
Differential operators on classical invariant rings do not lift modulo
Jack Jeffries, Anurag K. Singh
Levasseur and Stafford described the rings of differential operators on various classical invariant rings of characteristic zero; in each of the cases that they considered, the dif…
Extensions of primes, flatness, and intersection flatness
Melvin Hochster, Jack Jeffries
We study when has the property that prime ideals of extend to prime ideals or the unit ideal of , and the situation where this property continues to hold after adj…
Lower bounds on Hilbert--Kunz multiplicities and maximal F-signatures
Jack Jeffries, Yusuke Nakajima, Ilya Smirnov +2
Hilbert-Kunz multiplicity and F-signature are numerical invariants of commutative rings in positive characteristic that measure severity of singularities: for a regular ring both i…
Faithfulness of Top Local Cohomology Modules in Domains
Melvin Hochster, Jack Jeffries
We study the conditions under which the highest nonvanishing local cohomology module of a domain with support in an ideal is faithful over , i.e., which guarantee that $…
A transformation rule for natural multiplicities
Jack Jeffries, Ilya Smirnov
For multiplicities arising from a family of ideals we provide a general approach to transformation rules for a ring extension étale in codimension one. Our result can be applied to…
Quantifying singularities with differential operators
Holger Brenner, Jack Jeffries, Luis Núñez-Betancourt
The -signature of a local ring of prime characteristic is a numerical invariant that detects many interesting properties. For example, this invariant detects (non)singularity an…
Derived Functors of Differential Operators
Jack Jeffries
In their work on differential operators in positive characteristic, Smith and Van den Bergh define and study the derived functors of differential operators; they arise naturally as…
A Zariski-Nagata theorem for smooth -algebras
Alessandro De Stefani, Eloísa Grifo, Jack Jeffries
In a polynomial ring over a perfect field, the symbolic powers of a prime ideal can be described via differential operators: a classical result by Zariski and Nagata says that the…
Polarization of Neural Rings
Sema Gunturkun, Jack Jeffries, Jeffrey Sun
The "neural code" is the way the brain characterizes, stores, and processes information. Unraveling the neural code is a key goal of mathematical neuroscience. Topology, coding the…
Local Okounkov bodies and limits in prime characteristic
Daniel J. Hernández, Jack Jeffries
This article is concerned with the asymptotic behavior of certain sequences of ideals in rings of prime characteristic. These sequences, which we call -families of ideals, are u…
Mapping toric varieties into low dimensional spaces
Emilie Dufresne, Jack Jeffries
A smooth -dimensional projective variety can always be embedded into -dimensional space. In contrast, a singular variety may require an arbitrary large ambient space.…
On the behavior of singularities at the -pure threshold
Eric Canton, Daniel Hernández, Karl Schwede +6
We provide a family of examples where the -pure threshold and the log canonical threshold of a polynomial are different, but where does not divide the denominator of the …
Separating Invariants and Local Cohomology
Emilie Dufresne, Jack Jeffries
The study of separating invariants is a recent trend in invariant theory. For a finite group acting linearly on a vector space, a separating set is a set of invariants whose elemen…