Openness of splinter loci in prime characteristic

DOI10.1016/j.jalgebra.2023.03.025zbMath1525.13006arXiv2103.10525OpenAlexW3137041325MaRDI QIDQ6155815

Publication date: 7 June 2023

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.10525

zbMATH Keywords

plus closure Frobenius splitting absolute integral closure trace ideals $F$-purity uniformly $F$-compatible ideals splinter approximately Gorenstein rings algebra closures open loci

Mathematics Subject Classification ID

Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35) Cohen-Macaulay modules (13C14) Étale and flat extensions; Henselization; Artin approximation (13B40)

Related Items (2)

Globally $+$-regular varieties and the minimal model program for threefolds in mixed characteristic ⋮ The Cartier core map for Cartier algebras

Cites Work

On the number of compatibly Frobenius split subvarieties, prime $F$-ideals, and log canonical centers
Galois extensions, plus closure, and maps on local cohomology
$F$-adjunction
Globally $F$-regular and log Fano varieties
Centers of $F$-purity
The Frobenius structure of local cohomology
Frobenius splitting and cohomology vanishing for Schubert varieties
Splitting in integral extensions, Cohen-Macaulay modules and algebras
The purity of the Frobenius and local cohomology
Nagata's criterion and openness of loci for Gorenstein and complete intersection
Formal fibers and openness of loci
Separable integral extensions and plus closure
Tight closure of parameter ideals
On the direct summand conjecture and its derived variant
The direct factor conjecture
The vanishing conjecture for maps of Tor and derived splinters
Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay
The direct summand conjecture in dimension three.
Openness of the F-rational locus and smooth base change
Valuation rings are derived splinters
Canonical elements in local cohomology modules and the direct summand conjecture
Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Séconde partie)
Non-openness of loci in Noetherian rings
On the commutation of the test ideal with localization and completion
A survey of test ideals
F-Pure Homomorphisms, StrongF-regularity, andF-injectivity
Cartier modules: Finiteness results
F-rational rings have rational singularities
Upper bound of multiplicity of F-pure rings
Tight Closure, Invariant Theory, and the Briancon-Skoda Theorem
F-Purity and Rational Singularity
Two theorems on excellent rings
On Noetherian Rings of Characteristic p
Cyclic Purity Versus Purity in Excellent Noetherian Rings
Test ideals in quotients of $F$-finite regular local rings
A characterization of rational singularities in terms of injectivity of Frobenius maps
F-Regularity, Test Elements, and Smooth Base Change
TEST IDEALS IN RINGS WITH FINITELY GENERATED ANTI-CANONICAL ALGEBRAS
On a generalization of test ideals
Excellence in prime characteristic
ℚ-Gorenstein splinter rings of characteristic p are F-regular
Test Ideals in Local Rings
Test ideals via algebras of 𝑝^{-𝑒}-linear maps
Derived splinters in positive characteristic
Strong and weak F -regularity are equivalent for graded rings
On the canonical, fpqc, and finite topologies on affine schemes. The state of the art
Characteristic-free test ideals
F-singularities via alterations
Test Elements in Excellent Rings with an Application to the Uniform Artin- Rees Property
On the behavior of test ideals under finite morphisms
Characterizations of Regular Local Rings of Characteristic p
Contracted ideals from integral extensions of regular rings
A characterization of rational singularities
Extension of weakly and strongly F-regular rings by flat maps
Globally F-regular varieties: Applications to vanishing theorems for quotients of Fano varieties
On some permanence properties of (derived) splinters
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item

This page was built for publication: Openness of splinter loci in prime characteristic