\(\mathbb{A}^1\)-homotopy theory
From MaRDI portal
Publication:1129863
zbMath0907.19002MaRDI QIDQ1129863
Publication date: 24 August 1998
Published in: Documenta Mathematica (Search for Journal in Brave)
Full work available at URL: http://www.emis.de/journals/DMJDMV/xvol-icm/00/Voevodsky.MAN.html
Milnor conjecturealgebraic \(K\)-theoryalgebraic cobordismmotivic cohomologyhomotopy theory for schemes
Stable homotopy theory, spectra (55P42) Étale and other Grothendieck topologies and (co)homologies (14F20) Algebraic cycles and motivic cohomology ((K)-theoretic aspects) (19E15) Applications of methods of algebraic (K)-theory in algebraic geometry (14C35)
Related Items
Fundamental classes in motivic homotopy theory, On the push-forwards for motivic cohomology theories with invertible stable Hopf element, Motivic cohomology with \(\mathbb Z/2\)-coefficients, An overview of motivic homotopy theory, The motivic Segal-Becker theorem for algebraic \(K\)-theory, Stable étale realization and étale cobordism, Motives and homotopy theory in logarithmic geometry, Perverse, Hodge and motivic realizations of étale motives, Rigidity for linear framed presheaves and generalized motivic cohomology theories, The completion problem for equivariant \(K\)-theory, The unstable slice filtration, Vladimir Aleksandrovich Voevodsky, The six operations in equivariant motivic homotopy theory, Algebraic cobordism and étale cohomology, Motivic Brown-Peterson invariants of the rationals, Relationship between algebraic \(MSL\)-cobordisms and derived Witt groups, On the zeroth stable \( \mathbb{A}^1\)-homotopy group of a smooth projective variety, Comparison of cobordism theories, Operations on algebraic \(K\)-theory and regulators via the \(A^1\)-homotopy theory, Preorientations of the derived motivic multiplicative group, Trace and Künneth formulas for singularity categories and applications, Local duality in algebra and topology, Weight decompositions of Thom spaces of vector bundles in rational homotopy, On cellularization for simplicial presheaves and motivic homotopy, Transfers for ramified covering maps in homology and cohomology, Oka manifolds: from Oka to Stein and back, On the relation of symplectic algebraic cobordism to Hermitian \(K\)-theory, The Adams-Novikov spectral sequence and Voevodsky's slice tower, The Gysin triangle via localization and 𝐴¹-homotopy invariance, Product structures in motivic cohomology and higher Chow groups, Voevodsky's mixed motives versus Kontsevich's noncommutative mixed motives, A proof of the Grothendieck-Serre conjecture on principal bundles over regular local rings containing infinite fields, Continuous group actions on profinite spaces, ON THE MOTIVIC SPECTRAL SEQUENCE, Motivic twisted \(K\)-theory, Motivic Gauss-Bonnet formulas, Descent by blow-ups for homotopy invariant \(K\)-theory, The \(\mathbb{R}\)-local homotopy theory of smooth spaces, VANISHING IN STABLE MOTIVIC HOMOTOPY SHEAVES, Riemann-Roch for homotopy invariant \(K\)-theory and Gysin morphisms, Canonical<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi></mml:math>-deformations in arithmetic geometry, The Riemann-Roch theorem without denominators in motivic homotopy theory, The first stable homotopy groups of motivic spheres, Thick Ideals in Equivariant and Motivic Stable Homotopy Categories, Some Observations About Motivic Tensor Triangulated Geometry over a Finite Field, Coherence for invertible objects and multigraded homotopy rings, Motivic cohomology spectral sequence and Steenrod operations, Aspects of enumerative geometry with quadratic forms, Catégorie homotopique stable d’un site suspendu avec intervalle, Mathematical models of abstract systems: knowing abstract geometric forms, Motivic Steenrod operations in characteristicp, Unnamed Item, SL-oriented cohomology theories, Lectures on quadratic enumerative geometry, A motivic Segal theorem for pairs (announcement), On the Riemann-Roch formula without projective hypotheses, Framed motives of algebraic varieties (after V. Voevodsky), Algebraic slice spectral sequences, Modules over motivic cohomology, Homotopy-Theoretic Models of Type Theory, Picard groups, weight structures, and (noncommutative) mixed motives, Primes and fields in stable motivic homotopy theory, Higher traces, noncommutative motives, and the categorified Chern character, On the zeroth stable \(\mathbb{A}^1\)-homotopy group of a smooth curve, The \(\ell \)-adic trace formula for dg-categories and Bloch's conductor conjecture, Rigidity for henselian local rings and \(\mathbb{A}^1\)-representable theories, Spectra, spectra, spectra -- tensor triangular spectra versus Zariski spectra of endomorphism rings, Spanier-Whitehead duality in algebraic geometry, Homotopy theory of graphs, Equivariant cobordism for torus actions, A multiplicative \(K\)-theoretic model of Voevodsky's motivic \(K\)-theory spectrum, Motivic strict ring models for 𝐾-theory, The stable \(\mathbb{A}^1\)-connectivity theorems, Vladimir Voevodsky—An appreciation, The stable Galois correspondence for real closed fields, Recent developments on noncommutative motives, Tilting theory via stable homotopy theory, The motivic cofiber of \(\tau\), Filter quotients and non-presentable \((\infty,1)\)-toposes, On the relation of Voevodsky's algebraic cobordism to Quillen's \(K\)-theory, Traces in oriented homology theories of algebraic varieties, Higher symmetries in abstract stable homotopy theories, Degeneracy of some derived categories, On very effective Hermitian \(K\)-theory, \(\mathbb A^1\)-homotopy groups, excision, and solvable quotients, Galois equivariance and stable motivic homotopy theory, On universal stably free modules in positive characteristic, Artin motives, weights, and motivic nearby sheaves, Homotopy theory and arithmetic geometry -- motivic and Diophantine aspects: an introduction, An introduction to \(\mathbb{A}^1\)-enumerative geometry. Based on lectures by Kirsten Wickelgren delivered at the LMS-CMI research school ``Homotopy theory and arithmetic geometry -- motivic and Diophantine aspects, Cohomological methods in intersection theory, \(\mathbb{A}^1\)-homotopy theory and contractible varieties: a survey, Brown-Peterson spectra in stable \(\mathbb{A}^1\)-homotopy theory, Algebraic elliptic cohomology theory and flops. I, Motivic spectral sequence for relative homotopy K-theory, Stable \(\mathbb{A}^1\)-connectivity over a base, Semitopologization in motivic homotopy theory and applications, Quaternionic Grassmannians and Borel classes in algebraic geometry, The separable transfer, Rigidity for orientable functors, THE BOREL CHARACTER, Orientations and transfers in cohomology of algebraic varieties, Endomorphisms of the projective plane and the image of the Suslin-Hurewicz map, Fibrant resolutions for motivic Thom spectra, Lattice vertex algebras and loop Grassmannians, On the motivic Segal conjecture, Motivic cohomology, A Hochschild-Kostant-Rosenberg theorem and residue sequences for logarithmic Hochschild homology, Periodic self maps and thick ideals in the stable motivic homotopy category over \(\mathbb{C}\) at odd primes, Cellular objects in isotropic motivic categories, A motivic construction of the de Rham-Witt complex, THE UNIT MAP OF THE ALGEBRAIC SPECIAL LINEAR COBORDISM SPECTRUM, \(\mathbb{A}^1\)-homotopy theory of schemes, Riemann--Roch theorem for operations in cohomology of algebraic varieties, Spectra and symmetric spectra in general model categories, On the motivic commutative ring spectrum $\mathbf {BO}$, A telescope comparison lemma for THH., Transfinite Adams representability, Symmetric powers in abstract homotopy categories, Slices of co-operations forKGL, On the algebraic cobordism spectra 𝐌𝐒𝐋 and 𝐌𝐒𝐩
