Cdh descent for homotopy Hermitian \(K\)-theory of rings with involution

DOI10.25537/dm.2021v26.1275-1327zbMath1483.19003arXiv2009.09124MaRDI QIDQ2232379

Daniel Carmody

Publication date: 5 October 2021

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

Full work available at URL: https://arxiv.org/abs/2009.09124

zbMATH Keywords

Hermitian \(K\)-theorystable equivariant motivic homotopy theory

Mathematics Subject Classification ID

Motivic cohomology; motivic homotopy theory (14F42) Hermitian (K)-theory, relations with (K)-theory of rings (19G38)

Cites Work

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• The six operations in equivariant motivic homotopy theory
• Hermitian \(K\)-theory, derived equivalences and Karoubi's fundamental theorem
• The homotopy limit problem for Hermitian \(K\)-theory, equivariant motivic homotopy theory and motivic real cobordism
• Quadratic forms over semilocal rings
• Algebraic \(K\)-theory and descent for blow-ups
• \(A^1\)-representability of hermitian \(K\)-theory and Witt groups
• Descent by blow-ups for homotopy invariant \(K\)-theory
• cdh descent in equivariant homotopy \(K\)-theory
• Involutions of Azumaya algebras
• A transfer morphism for Hermitian \(K\)-theory of schemes with involution
• Geometric models for higher Grothendieck-Witt groups in \(\mathbb A^1\)-homotopy theory
• Surgery of non-simply-connected manifolds
• Motivic homotopy theory of group scheme actions
• \(\mathbb{A}^1\)-homotopy theory of schemes
• Stacks and the homotopy theory of simplicial sheaves

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