skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • Home
  • Search Results
  • Page 1 of 2

Search for: All records

Creators/Authors contains: "Jeffries, Jack"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; (, American Journal of Mathematics)
    abstract: 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 affine algebras over a complete local algebra over a mixed characteristic discrete valuation ring. The result makes use of the minors of a matrix that includes a row coming from the values of a $$p$$-derivation. To study the analogue of modules of differentials associated with the mixed Jacobian matrices that arise in our context, we introduce and investigate the notion of a {\it perivation}, which may be thought of, roughly, as a linearization of the notion of $$p$$-derivation. We also develop a mixed characteristic analogue of the positive characteristic $$\Gamma$$-construction, and apply this to give additional nonsingularity criteria. 
    more » « less
    Free, publicly-accessible full text available December 1, 2025
  2. ; ; (, Transformation Groups)
    Full Text Available 
  3. (, Notices of the American Mathematical Society)
    Full Text Available 
  4. ; (, Advances in Mathematics)
    Full Text Available 
  5. ; ; ; ; ; ; (, Michigan Mathematical Journal)
    Full Text Available 
  6. ; ; (, Transactions of the American Mathematical Society)
    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 various algebraic and topological aspects of the singularities of the vanishing locus. Work of Mustaţă, later extended by Bitoun and the third author, provides an analogous Bernstein-Sato theory for regular rings of positive characteristic. In this paper, we extend this theory to singular ambient rings in positive characteristic. We establish finiteness and rationality results for Bernstein-Sato roots for large classes of singular rings, and relate these roots to other classes of numerical invariants defined via the Frobenius map. We also obtain a number of new results and simplified arguments in the regular case. 
    more » « less
    Full Text Available 
  7. ; ; (, Collectanea Mathematica)
    Abstract We initiate the study of the resolution of singularities properties of Nash blowups over fields of prime characteristic. We prove that the iteration of normalized Nash blowups desingularizes normal toric surfaces. We also introduce a prime characteristic version of the logarithmic Jacobian ideal of a toric variety and prove that its blowup coincides with the Nash blowup of the variety. As a consequence, the Nash blowup of a, not necessarily normal, toric variety of arbitrary dimension in prime characteristic can be described combinatorially. 
    more » « less
  8. ; ; ; ; (, Mathematical Proceedings of the Cambridge Philosophical Society)
    Abstract 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 invariants are equal to one and the converse holds under mild assumptions. A natural question is for what singular rings these invariants are closest to one. For Hilbert–Kunz multiplicity this question was first considered by the last two authors and attracted significant attention. In this paper, we study this question, i.e., an upper bound, for F-signature and revisit lower bounds on Hilbert–Kunz multiplicity. 
    more » « less
    Full Text Available 
  9. ; ; ; (, Forum of Mathematics, Sigma)
    Full Text Available 
  10. ; ; (, Mathematische Zeitschrift)
    Full Text Available