Topological Hochschild cohomology and generalized Morita equivalence.

DOI10.2140/agt.2004.4.623zbMath1078.16005arXivmath/0209003OpenAlexW2125449300MaRDI QIDQ1880646

Andrey Lazarev, Andrew Baker

Publication date: 30 September 2004

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0209003

zbMATH Keywords

spectraAzumaya algebrashomotopy categoriesMorita theorytopological Hochschild cohomology

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Ext and Tor, generalizations, Künneth formula (category-theoretic aspects) (18G15) Abstract and axiomatic homotopy theory in algebraic topology (55U35) Spectra with additional structure ((E_infty), (A_infty), ring spectra, etc.) (55P43) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05)

Related Items

Brauer groups for commutative \(S\)-algebras ⋮ Topological Hochschild homology and cohomology of \(A_{\infty }\) ring spectra ⋮ Brauer groups and étale cohomology in derived algebraic geometry ⋮ Azumaya objects in triangulated bicategories ⋮ Homotopy theory of spectral categories

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Duality in algebra and topology
• Equivariant stable homotopy theory. With contributions by J. E. McClure
• Hochschild cohomology and moduli spaces of strongly homotopy associative algebras
• Stable model categories are categories of modules
• On the \(\Gamma\)-cohomology of rings of numerical polynomials and \(E_\infty\) structures on \(K\)-theory
• On the structure of 𝑃(𝑛)_{∗}𝑃((𝑛)) for 𝑝=2
• Complete modules and torsion modules
• The Brauer Group of a Commutative Ring
• Realizability of algebraic Galois extensions by strictly commutative ring spectra
• A∞ STRUCTURES ON SOME SPECTRA RELATED TO MORAVA K-THEORIES
• Products on 𝑀𝑈-modules
• Axiomatic stable homotopy theory
• Towers of MU-Algebras and the Generalized Hopkins–Miller theorem
• Symmetric spectra
• On the Topological Hochschild Homology of bu, I
• On the Adams spectral sequence for \(R\)-modules
• The Picard group of equivariant stable homotopy theory