Motivic cell structures

Abstract

An object in motivic homotopy theory is called cellular if it can be built out of motivic spheres using homotopy colimit constructions. We explore some examples and consequences of cellularity. We explain why the algebraic K-theory and algebraic cobordism spectra are both cellular, and prove some Kunneth theorems for cellular objects.

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-26.abs.html

References in corpus (1)

• Algebras and modules in monoidal model categories

Cited by in corpus (50)

• From algebraic cobordism to motivic cohomology
• The motive of a classifying space
• Slices of hermitian K-theory and Milnor's conjecture on quadratic forms
• Mixed Weil cohomologies
• Local duality in algebra and topology
• Orientation theory in arithmetic geometry
• C_2-equivariant stable homotopy from real motivic stable homotopy
• The Adams-Novikov spectral sequence and Voevodsky's slice tower
• The intersection motive of the moduli stack of shtukas
• Motivic Hopf elements and relations
• Yang-Mills theory and Tamagawa numbers
• Local duality for structured ring spectra
• Two-complete stable motivic stems over finite fields
• Chern classes, K-theory and Landweber exactness over nonregular base schemes
• Ext and the Motivic Steenrod Algebra over $\mathbb{R}$
• Exotic Motivic Periodicities
• Euler class groups and motivic stable cohomotopy
• The motivic Adams-Novikov spectral sequence at odd primes over $\mathbb{C}$ and $\mathbb{R}$
• Equivariant motivic homotopy theory
• On equivariant and motivic slices
• Motivic connective K-theories and the cohomology of A(1)
• Cellularity of hermitian K-theory and Witt theory
• Adjoint functors on the derived category of motives
• More examples of motivic cell structures
• Algebraic Cobordism and Étale Cohomology
• Motivic twisted K-theory
• Primes and fields in stable motivic homotopy theory
• The Simplicial EHP Sequence in A1-Algebraic Topology
• A generalization of Ohkawa's theorem
• Comparing localizations across adjunctions
• Topological models for stable motivic invariants of regular number rings
• The homotopy limit problem and the cellular Picard group of Hermitian $K$-theory
• Algebraic vector bundles and $p$-local A^1-homotopy theory
• Relations between slices and quotients of the algebraic cobordism spectrum
• The motivic Adams spectral sequence
• Motivic and Étale Spanier-Whitehead duality and the Becker-Gottlieb transfer
• Borel isomorphism and absolute purity
• Stable motivic pi_1 of low-dimensional fields
• An $\mathbb{R}$-motivic $v_1-$self-map of periodicity $1$
• Galois reconstruction of Artin-Tate $\mathbb{R}$-motivic spectra
• The Motivic Cohomology of Stiefel Varieties
• The Gm-equivariant Motivic Cohomology of Stiefel Varieties
• $T$-equivariant motives of flag varieties
• Motivic Cell Structures for Spherical Varieties
• Motivic cohomology and infinitesimal group schemes
• Moduli stack of oriented formal groups and cellular motivic spectra over $\mathbf{C}$
• Squaring operations in the $RO(C_2)$-graded and real motivic Adams spectral sequences
• A cellular absolute motivic ring spectrum representing Hermitian K-theory
• Embedding of category of twisted Chow-Witt correspondences into geometric stable $\A^1$-derived category over a field
• Inverting the Hopf map