Local cohomological dimension in characteristic p

DOI10.2307/1971025zbMath0362.14002OpenAlexW2082020453MaRDI QIDQ1239773

Robin Hartshorne, Robert Speiser

Publication date: 1977

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/1971025

Mathematics Subject Classification ID

Local ground fields in algebraic geometry (14G20) Local cohomology and algebraic geometry (14B15)

Related Items (79)

Local cohomology multiplicities in terms of étale cohomology ⋮ Complex subspaces of homogeneous complex manifolds II—Homotopy Results ⋮ Global parameter test ideals ⋮ Frobenius test exponent for ideals generated by filter regular sequences ⋮ Surjectivity of some local cohomology map and the second vanishing theorem ⋮ Graded annihilators of modules over the Frobenius skew polynomial ring, and tight closure ⋮ On the uniform bound of Frobenius test exponents ⋮ Local Cohomology—An Invitation ⋮ The finiteness dimension of local cohomology modules and its dual notion ⋮ Cofiniteness and vanishing of local cohomology modules ⋮ Frobenius test exponents for parameter ideals in generalized Cohen-Macaulay local rings ⋮ Cohomologically Full Rings ⋮ Nilpotence of Frobenius action and the Hodge filtration on local cohomology ⋮ Local cohomology modules supported at determinantal ideals ⋮ Local cohomology and F-stability ⋮ On the discreteness and rationality of \(F\)-jumping coefficients ⋮ Graded annihilators and tight closure test ideals ⋮ Tight closure test exponents for certain parameter ideals ⋮ Absolute integral closure in positive characteristic ⋮ A prime-characteristic analogue of a theorem of Hartshorne-Polini ⋮ On the number of compatibly Frobenius split subvarieties, prime \(F\)-ideals, and log canonical centers ⋮ Nilpotence of Frobenius actions on local cohomology and Frobenius closure of ideals ⋮ A unified approach to formal local cohomology and local Tate cohomology ⋮ Tight closure of parameter ideals in local rings \(F\)-rational on the punctured spectrum ⋮ On the Frobenius closure of parameter ideals in local rings F-injective on the punctured spectrum ⋮ A remark on the category of graded 𝐹-modules ⋮ Discreteness of 𝐹-jumping numbers at isolated non-ℚ-Gorenstein points ⋮ Some properties and applications of \(F\)-finite \(F\)-modules ⋮ A connectedness result in positive characteristic ⋮ Topological calculation of local cohomological dimension ⋮ Globally \(+\)-regular varieties and the minimal model program for threefolds in mixed characteristic ⋮ \(F\)-nilpotent rings and permanence properties ⋮ Big tight closure test elements for some non-reduced excellent rings ⋮ TEST IDEALS IN RINGS WITH FINITELY GENERATED ANTI-CANONICAL ALGEBRAS ⋮ Finite generation of nilpotent quotients of fundamental groups of punctured spectra ⋮ Rees algebras and generalized depth‐like conditions in prime characteristic ⋮ Lyubeznik numbers of projective schemes ⋮ Varieties of small codimension in projective space ⋮ The saturation of frobenius powers of ideals ⋮ On cohomological dimension and depth under linkage ⋮ The mathematical contributions of Craig Huneke ⋮ Local cohomology modules of a smooth \(\mathbb{Z}\)-algebra have finitely many associated primes ⋮ Notes on the Frobenius test exponents ⋮ Unnamed Item ⋮ The Frobenius homomorphism, and local cohomology in regular local rings of positive characteristic ⋮ Galois extensions, plus closure, and maps on local cohomology ⋮ Right and left modules over the Frobenius skew polynomial ring in theF-finite case ⋮ Bass Numbers of Local Cohomology Modules ⋮ Cartier modules on toric varieties ⋮ Test ideals via algebras of 𝑝^{-𝑒}-linear maps ⋮ A note on the use of Frobenius map and D-modules in local cohomology ⋮ \(F\)-signature and Hilbert-Kunz multiplicity: a combined approach and comparison ⋮ A dual to tight closure theory ⋮ Connectivity of joins, cohomological quantifier elimination, and an algebraic Toda's theorem ⋮ Discreteness and rationality of \(F\)-jumping numbers on singular varieties ⋮ Some applications of the Frobenius in characteristic 0 ⋮ An excellent $F$-pure ring of prime characteristic has a big tight closure test element ⋮ On a Grauert-Riemenschneider vanishing theorem for Frobenius split varieties in characteristic \(p\) ⋮ Bockstein homomorphisms in local cohomology ⋮ The structure of one-dimensional F-pure rings ⋮ $D$-module and $F$-module length of local cohomology modules ⋮ Unnamed Item ⋮ On the arithmetic of tight closure ⋮ On the vanishing of local cohomology modules ⋮ Upper bound of multiplicity in prime characteristic ⋮ Positive characteristic algebraic geometry ⋮ Cartier modules: Finiteness results ⋮ A sufficient condition for the finiteness of Frobenius test exponents ⋮ Estimates forF-jumping numbers and bounds for Hartshorne–Speiser–Lyubeznik numbers ⋮ On the arithmetical rank of certain segre embeddings ⋮ Cohomological and projective dimensions ⋮ Algorithmic computation of local cohomology modules and the local cohomological dimension of algebraic varieties ⋮ On the Hartshorne–Speiser–Lyubeznik theorem about Artinian modules with a Frobenius action ⋮ On the attached prime ideals of certain Artinian local cohomology modules ⋮ On the attached prime ideals of certain Artinian local cohomology modules ⋮ Uniform behaviour of the Frobenius closures of ideals generated by regular sequences ⋮ Homological properties of pinched Veronese rings ⋮ \(F^e\)-modules with applications to \(D\)-modules ⋮ Finiteness properties of local cohomology modules (an application of \(D\)- modules to commutative algebra)

This page was built for publication: Local cohomological dimension in characteristic p