Remarks on motivic homotopy theory over algebraically closed fields

DOI10.1017/is010001012jkt098zbMath1248.14026OpenAlexW2170433531MaRDI QIDQ3002215

Igor Kriz, Po Hu, Kyle M. Ormsby

Publication date: 20 May 2011

Published in: Journal of K-Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/is010001012jkt098

zbMATH Keywords

motivic homotopy theoryAdams spectral sequencesAdams-Novikov spectral sequencesmotivic cobordism theories, \(J\)-homomorphism

Mathematics Subject Classification ID

Adams spectral sequences (55T15) Motivic cohomology; motivic homotopy theory (14F42) (J)-homomorphism, Adams operations (19L20)

Related Items (23)

An overview of motivic homotopy theory ⋮ \(\mathbb{C}\)-motivic modular forms ⋮ Motivic Brown-Peterson invariants of the rationals ⋮ The structure of motivic homotopy groups ⋮ Stable motivic \(\pi_1\) of low-dimensional fields ⋮ Ext and the motivic Steenrod algebra over \(\mathbb R\) ⋮ Stable homotopy groups of spheres: from dimension 0 to 90 ⋮ Stable homotopy groups ⋮ The homotopy limit problem for Hermitian \(K\)-theory, equivariant motivic homotopy theory and motivic real cobordism ⋮ VANISHING IN STABLE MOTIVIC HOMOTOPY SHEAVES ⋮ New families in the homotopy of the motivic sphere spectrum ⋮ Synthetic spectra and the cellular motivic category ⋮ Some Observations About Motivic Tensor Triangulated Geometry over a Finite Field ⋮ Convergence of the Motivic Adams Spectral Sequence ⋮ Motivic connectiveK-theories and the cohomology of A(1) ⋮ The motivic Adams spectral sequence ⋮ Isotropic stable motivic homotopy groups of spheres ⋮ The motivic cofiber of \(\tau\) ⋮ Stable Stems ⋮ $kq$-resolutions I ⋮ The Chow \(t\)-structure on the \(\infty\)-category of motivic spectra ⋮ Some comments on motivic nilpotence ⋮ The \(\eta\)-local motivic sphere

Cites Work

• The localization of spectra with respect to homology
• On the K-theory of algebraically closed fields
• Algebraic Morava \(K\)-theories
• On the Picard group of the stable \(\mathbb A^1\)-homotopy category
• \(A^1\)-representability of hermitian \(K\)-theory and Witt groups
• Reduced power operations in motivic cohomology
• On the groups \(J(X)\). II
• On the groups \(J(X)\). IV
• On the cohomology and K-theory of the general linear groups over a finite field
• Motivic cell structures
• On the groups \(J(X)\). I
• Cobordisme algébrique I
• Cobordisme algébrique II
• Suite spectrale d'Adams et invariants cohomologiques des formes quadratiques
• \(\mathbb{A}^1\)-homotopy theory of schemes

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