Homology of algebraic varieties: An introduction to the works of Suslin and Voevodsky

DOI10.1090/S0273-0979-97-00723-4zbMath0888.19001MaRDI QIDQ4372762

Marc N. Levine

Publication date: 16 December 1997

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

\(K\)-theoryBloch-Kato conjectureétale cohomologyQuillen-Lichtenbaum conjecturealgebraic cycleslocalization propertymotivic cohomologyChow groupGrothendieck topology

Mathematics Subject Classification ID

Étale and other Grothendieck topologies and (co)homologies (14F20) Algebraic cycles (14C25) Relations of (K)-theory with cohomology theories (19E20) (K)-theory of schemes (19E08) Algebraic cycles and motivic cohomology ((K)-theoretic aspects) (19E15) Grothendieck topologies and Grothendieck topoi (18F10) Research exposition (monographs, survey articles) pertaining to (K)-theory (19-02)

Related Items (2)

Homology of linear groups via cycles in \(BG\times X\) ⋮ Voevodsky’s proof of Milnor’s conjecture

Cites Work

• On equivalence classes of cycles in an algebraic variety
• Quasifaserungen und unendliche symmetrische Produkte
• On the K-theory of local fields
• Homology of the infinite orthogonal and symplectic groups over algebraically closed fields. An appendix to the paper of A. Suslin
• Etale K-theory. I: Connections with etale cohomology and algebraic vector bundles
• The K-theory of strict Hensel local rings and a theorem of Suslin
• Algebraic cycles and higher K-theory
• Moving algebraic cycles of bounded degree
• Correspondence homomorphisms for singular varieties
• Smoothness, semi-stability and alterations
• The torsion of the group of 0-cycles modulo rational equivalence
• Weight filtrations via commuting automorphisms
• Mixed motives and algebraic cycles. I
• Singular homology of abstract algebraic varieties
• Homology of schemes
• Rational equivalence of O-cycles on surfaces
• Duality relating spaces of algebraic cocycles and cycles
• Le théorème de Riemann-Roch
• La théorie des classes de Chern
• Étale $K$-theory. II. Connections with algebraic $K$-theory
• Algebraic and Etale K-Theory
• Values of zeta-functions at non-negative integers
• Higher algebraic K-theory: I
• $K$-théorie algébrique et $K$-théorie topologique I.
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