scholarly journals Nash blowups in prime characteristic

2021 ◽  
Author(s):  
Daniel Duarte ◽  
Luis Núñez-Betancourt
Keyword(s):  
Prime Characteristic

Frobenius closure and prime characteristic singularities

2020 ◽  
Author(s):  
◽  
Kyle Logan Maddox
Keyword(s):  
Local Ring ◽  
Local Cohomology ◽  
Sufficient Condition ◽  
Zariski Topology ◽  
Prime Characteristic ◽  
Joint Work ◽  
University Of Missouri ◽  
Mild Conditions ◽  
Flat Maps ◽  
The University

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] This dissertation outlines several results about prime characteristic singularities for which the nilpotent part under the induced Frobenius action on local cohomology is either finite colength or the entire module, collectively referred to here as nilpotent singularities. First, we establish a sufficient condition for the finiteness of the Frobenius test exponent for a local ring and apply it to conclude that nilpotent singularities have finite Frobenius test exponent. In joint work with Jennifer Kenkel, Thomas Polstra, and Austyn Simpson, we show that under mild conditions nilpotent singularities descend and ascend along faithfully flat maps. Consequently, we then prove that the loci of primes which are weakly F-nilpotent and F-nilpotent are open in the Zariski topology for rings which are either F-finite or essentially of fiiite type over an excellent local ring.

scholarly journals DERIVATIONS OF THE ODD CONTACT LIE ALGEBRAS IN PRIME CHARACTERISTIC

2013 ◽  
Vol 50 (3) ◽  
pp. 591-605
Author(s):  
Yan Cao ◽  
Xiumei Sun ◽  
Jixia Yuan
Keyword(s):  
Lie Algebras ◽  
Prime Characteristic

scholarly journals Multiplicity bounds in prime characteristic

2019 ◽  
Vol 47 (6) ◽  
pp. 2450-2456 ◽  
Author(s):  
Mordechai Katzman ◽  
Wenliang Zhang
Keyword(s):  
Prime Characteristic

scholarly journals On a generalization of test ideals

2004 ◽  
Vol 175 ◽  
pp. 59-74 ◽  
Author(s):  
Nobuo Hara ◽  
Shunsuke Takagi
Keyword(s):  
Prime Characteristic ◽  
Tight Closure ◽  
Test Ideal ◽  
Important Object ◽  
The Ideal

AbstractThe test ideal τ(R) of a ring R of prime characteristic is an important object in the theory of tight closure. In this paper, we study a generalization of the test ideal, which is the ideal τ(at) associated to a given ideal a with rational exponent t ≥ 0. We first prove a key lemma of this paper (Lemma 2.1), which gives a characterization of the ideal τ(at). As applications of this key lemma, we generalize the preceding results on the behavior of the test ideal τ(R). Moreover, we prove an analogue of so-called Skoda’s theorem, which is formulated algebraically via adjoint ideals by Lipman in his proof of the “modified Briançon-Skoda theorem.”

scholarly journals BERNSTEIN–SATO ROOTS FOR MONOMIAL IDEALS IN POSITIVE CHARACTERISTIC

2020 ◽  
pp. 1-10
Author(s):  
EAMON QUINLAN-GALLEGO
Keyword(s):  
Positive Characteristic ◽  
Monomial Ideals ◽  
Prime Characteristic ◽  
The Ideal

Following the work of Mustaţă and Bitoun, we recently developed a notion of Bernstein–Sato roots for arbitrary ideals, which is a prime characteristic analogue for the roots of the Bernstein–Sato polynomial. Here, we prove that for monomial ideals the roots of the Bernstein–Sato polynomial (over $\mathbb{C}$ ) agree with the Bernstein–Sato roots of the mod $p$ reductions of the ideal for $p$ large enough. We regard this as evidence that the characteristic- $p$ notion of Bernstein–Sato root is reasonable.

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