Cohomological and projective dimensions

DOI10.1112/S0010437X12000899zbMath1290.13012arXiv1204.3280OpenAlexW2166505507MaRDI QIDQ2841771

Matteo Varbaro

Publication date: 30 July 2013

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.3280

zbMATH Keywords

projective dimensioncohomological dimensiondepthlocal cohomologyperfect ideals

Mathematics Subject Classification ID

Vanishing theorems in algebraic geometry (14F17) Local cohomology and commutative rings (13D45)

Related Items (15)

Hodge filtration on local cohomology, Du Bois complex and local cohomological dimension ⋮ Surjectivity of some local cohomology map and the second vanishing theorem ⋮ Local Cohomology—An Invitation ⋮ Cohomologically Full Rings ⋮ When does depth stabilize early on? ⋮ Vanishing of local cohomology and set-theoretically Cohen-Macaulay ideals ⋮ Topological calculation of local cohomological dimension ⋮ On the relationship between depth and cohomological dimension ⋮ Local cohomology of Du Bois singularities and applications to families ⋮ A generalized Serre’s condition ⋮ Cohomological dimensions of specialization-closed subsets and subcategories of modules ⋮ Regularity of line configurations ⋮ Cohomological dimension, Lyubeznik numbers, and connectedness in mixed characteristic ⋮ An extension of a theorem of Hartshorne ⋮ Connectedness and Lyubeznik Numbers

Uses Software

• Macaulay2

Cites Work

• Algebraic geometry over the complex numbers
• On the vanishing of local cohomology modules
• Dimension projective finie et cohomologie locale. Applications à la demonstration de conjectures de M. Auslander, H. Bass et A. Grothendieck
• Algebraic geometry and analytic geometry
• Local cohomological dimension of algebraic varieties
• Local cohomological dimension in characteristic p
• Finiteness properties of local cohomology modules (an application of \(D\)- modules to commutative algebra)
• Cohomological dimension of algebraic varieties
• Ample subvarieties of algebraic varieties. Notes written in collaboration with C. Musili
• What makes a complex exact?
• On the arithmetical rank of certain segre embeddings
• On the vanishing of local cohomology in characteristic p > 0
• Complete Intersections and Connectedness
• The Number of Equations Defining a Determinantal Variety
• Characterizations of Regular Local Rings of Characteristic p
• On the De Rham cohomology of algebraic varieties

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