Local duality in algebra and topology

DOI10.1016/j.aim.2018.07.017zbMath1403.55008arXiv1511.03526OpenAlexW2121510182WikidataQ129558229 ScholiaQ129558229MaRDI QIDQ1669043

Gabriel Valenzuela, Tobias Barthel, Drew Heard

Publication date: 29 August 2018

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.03526

zbMATH Keywords

local cohomologycomodulesinfinity categorieschromatic homotopy theorylocal duality

Mathematics Subject Classification ID

Localization and completion in homotopy theory (55P60) Local cohomology and commutative rings (13D45) Local cohomology and algebraic geometry (14B15) Abstract and axiomatic homotopy theory in algebraic topology (55U35) Duality in applied homological algebra and category theory (aspects of algebraic topology) (55U30)

Related Items (17)

Separated and complete adelic models for one-dimensional Noetherian tensor-triangulated categories ⋮ The left localization principle, completions, and cofree \(G\)-spectra ⋮ The \(Sp_{k,n}\)-local stable homotopy category ⋮ Applications of reduced and coreduced modules I ⋮ \(C_2\)-equivariant stable homotopy from real motivic stable homotopy ⋮ The \(v_1\)-periodic region in the cohomology of the \(\mathbb{C}\)-motivic Steenrod algebra ⋮ Injective DG-modules over non-positive DG-rings ⋮ The algebraic chromatic splitting conjecture for Noetherian ring spectra ⋮ The homotopy limit problem and the cellular Picard group of Hermitian \(K\)-theory ⋮ Derived completion for comodules ⋮ Monochromatic homotopy theory is asymptotically algebraic ⋮ The homotopy theory of complete modules ⋮ Completion and torsion over commutative DG rings ⋮ Stratification and duality for homotopical groups ⋮ Localizing the \(E_2\) page of the Adams spectral sequence ⋮ RATIONAL LOCAL SYSTEMS AND CONNECTED FINITE LOOP SPACES ⋮ Torsion models for tensor-triangulated categories: the one-step case

Cites Work

• Deriving Auslander's formula
• Nilpotence and descent in equivariant stable homotopy theory
• \(K\)-theory and the bridge from motives to noncommutative motives
• Monoidality of Franke's exotic model
• Duality in algebra and topology
• Motivic Landweber exactness
• The derived category of quasi-coherent sheaves and axiomatic stable homotopy
• Complexes of injective \(kG\)-modules.
• Equivariant stable homotopy theory. With contributions by J. E. McClure
• Equivariant resolution, linearization, and Hilbert's fourteenth problem over arbitrary base schemes
• Nilpotence and stable homotopy theory. I
• \(\mathbb{A}^1\)-homotopy theory
• Derived functors of \(I\)-adic completion and local homology
• Morava stabilizer algebras and the localization of Novikov's \(E_2\)-term
• Algebraic Morava \(K\)-theories
• Secondary power operations and the Brown-Peterson spectrum at the prime \(2\)
• Comodules and Landweber exact homology theories
• Categorical equivalences and realization theorems
• Quasi-categories and Kan complexes
• Stable model categories are categories of modules
• \(\nu_n\) telescopes and the Adams spectral sequence
• On the homology of completion and torsion
• The stack of formal groups in stable homotopy theory
• Local duality for structured ring spectra
• Affine duality and cofiniteness
• Associated prime ideals and Hopf algebras
• Invertible modules for commutative \(\mathbb S\)-algebras with residue fields
• Motivic cell structures
• Centralizers in good groups are good
• Complete modules and torsion modules
• Motivic connectiveK-theories and the cohomology of A(1)
• Equivariant orthogonal spectra and 𝑆-modules
• HZ -algebra spectra are differential graded algebras
• Localization with Respect to Certain Periodic Homology Theories
• Studies in Duality on Noetherian Formal Schemes and Non-Noetherian Ordinary Schemes
• Nilpotence and Periodicity in Stable Homotopy Theory. (AM-128)
• Morava 𝐾-theories and localisation
• Local homology and cohomology on schemes
• Axiomatic stable homotopy theory
• Proregular sequences, local cohomology, and completion
• Invertible Spectra in the E (n )-Local Stable Homotopy Category
• Local cohomology of ${BP_{*}BP}$-comodules
• Sheafifiable homotopy model categories
• Morita theory for Hopf algebroids and presheaves of groupoids
• Foundations of Grothendieck Duality for Diagrams of Schemes
• Ind-abelian categories and quasi-coherent sheaves
• The multiplication on BP
• Higher Topos Theory (AM-170)
• the stable derived category of a noetherian scheme
• Nilpotence and stable homotopy theory. II
• \(\mathbb{A}^1\)-homotopy theory of schemes
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Local duality in algebra and topology