On 2-torsion in motivic cohomology
Vladimir Voevodsky
TL;DR
This paper proves the 2-torsion part of the Beilinson-Lichtenbaum conjectures in motivic cohomology, including the Milnor conjecture linking K-theory and Galois cohomology with Z/2 coefficients.
Contribution
It establishes the 2-local component of key conjectures in motivic cohomology, confirming the Milnor conjecture.
Findings
Proof of the 2-torsion part of the Beilinson-Lichtenbaum conjectures
Verification of the Milnor conjecture relating K-theory and Galois cohomology
Advancement in understanding motivic cohomology and torsion phenomena
Abstract
In this paper we prove the 2-local part of the Beilinson-Lichtenbaum conjectures on tosion in motivic cohomology. In particular we prove the Milnor conjecture relating Milnor's K-theory and the Galois cohomology with Z/2-coefficients. This paper is a new version of the previously distributed preprint "The Milnor Conjecture".
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology