Motivic cohomology: applications and conjectures
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Publication:5197954
DOI10.1090/suga/443zbMath1422.14001OpenAlexW2976746658WikidataQ123347922 ScholiaQ123347922MaRDI QIDQ5197954
Publication date: 2 October 2019
Published in: Sugaku Expositions (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/suga/443
Research exposition (monographs, survey articles) pertaining to number theory (11-02) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Algebraic cycles (14C25) Motivic cohomology; motivic homotopy theory (14F42)
Cites Work
- Tame class field theory for singular varieties over algebraically closed fields
- Comparison of dualizing complexes
- Rojtman's theorem for normal schemes
- Duality via cycle complexes
- On Suslin's singular homology and cohomology
- On motivic cohomology with \(\mathbb{Z}/l\)-coefficients
- Cohomological Hasse principle and motivic cohomology for arithmetic schemes
- Motivic cohomology over Dedekind rings
- Weil-étale cohomology over finite fields
- Einheiten und Divisorklassen in endlich erzeugbaren Körpern. (Units and divisor classes in finitely generated fields)
- Unramified class field theory over function fields in several variables
- The Bloch complex in codimension one and arithmetic duality
- An exact sequence for \(K^M_*/2\) with applications to quadratic forms
- Singular homology of arithmetic schemes
- Groupes de Chow et K-théorie de variétés sur un corps fini
- Gersten's conjecture for the K-theory with torsion coefficients of a discrete valuation ring
- Duality in the étale cohomology of one-dimensional proper schemes and generalizations
- Algebraic cycles and higher K-theory
- \(p\)-adic étale cohomology
- Milnor \(K\)-theory is the simplest part of algebraic \(K\)-theory
- Tate's conjecture, algebraic cycles and rational \(K\)-theory in characteristic \(p\)
- Kato homology of arithmetic schemes and higher class field theory over local fields
- \(K\)-theory of semi-local rings with finite coefficients and étale cohomology
- Tame class field theory for singular varieties over finite fields
- On the kernel of the reciprocity map of normal surfaces over finite fields
- The torsion of the group of 0-cycles modulo rational equivalence
- On the Albanese map for smooth quasi-projective varieties
- Singular homology of abstract algebraic varieties
- Artin-Verdier duality for arithmetic surfaces
- Duality for \(\mathbb Z\)-constructible sheaves on curves over finite fields
- The \(K\)-theory of fields in characteristic \(p\)
- Homological descent for motivic homology theories
- Unramified class field theory of arithmetical surfaces
- Norm varieties
- Arithmetic cohomology over finite fields and special values of \(\zeta\)-functions
- Endomorphisms of Abelian varieties over finite fields
- Rational equivalence of O-cycles on surfaces
- Algebraic \(K\)-theory and quadratic forms. With an appendix by J. Tate
- Schémas en groupes. II: Groupes de type multiplicatif, et structure des schémas en groupes généraux. Exposés VIII à XVIII. Séminaire de Géométrie Algébrique du Bois Marie 1962/64 (SGA 3) dirigé par Michel Demazure et Alexander Grothendieck. Revised reprint
- Finite generation conjectures for motivic cohomology theories over finite fields
- Sur le groupe des classes d’un schéma arithmétique
- Arithmetic homology and an integral version of Kato's conjecture
- Opérations En K-Théorie Algébrique
- A Hasse principle for two dimensional global fields.
- Values of Zeta Functions of Varieties Over Finite Fields
- Higher algebraic K-theory: I
- Stable real cohomology of arithmetic groups
- K2of artinian Q-algebras, with application to algebraic cycles
- Singular homology and class field theory of varieties over finite fields
- The Bloch-Kato conjecture and a theorem of Suslin-Voevodsky
- The Weil-étale topology on schemes over finite fields
- The spectral sequence relating algebraic K-theory to motivic cohomology
- The homotopy coniveau tower
- Hasse principles for higher-dimensional fields
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