Milnor K-theory
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General Introduction
See also Motivic cohomology
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Search results
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Online References
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Paper References
Chapter 7 of Gille and Szamuely (in Various folder under ALGEBRA)
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Definition
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Properties
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Standard theorems
The Milnor conjecture. See for example Kahn's Bourbaki account, reproduced in K-theory handbook, Vol 2.
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
Thomason: Le principe de scindage. He shows roughly that any theory for schemes satisfying certain axioms and mapping to Quillen K-theory, must be surjective when evaluated on the ground field . This implies that Milnor K-theory, if required to satisfy these axioms, cannot be extended to the category of varieties over .
Kerr: A regulator formula for Milnor K-groups (2003)
Motivic interpretation of Milnor K-groups attached to Jacobian varieties, by Satoshi Mochizuki: K0774
Müller-Stach and Elbaz-Vincent: Milnor K-theory of rings, higher Chow groups and applications
The Gersten conjecture for Milnor K-theory , by Moritz Kerz
MR2034645 (2004m:19003) Cathelineau, Jean-Louis(F-NICE-LD) Projective configurations, homology of orthogonal groups, and Milnor $K$-theory.
Milnor: Algebraic K-theory and quadratic forms (1969/70)
Totaro: Milnor K-theory is the simplest part of algebraic K-theory (1992)
Voevodsky, Vishik, Orlov: An exact sequence for mod 2 Milnor K-th etc. Contains an exact seq for the multiplication in mod 2 Milnor Kth with an element, and applications to questions on quadratic forms, e.g. the Milnor conjecture and the J-filtration conjecture.
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Other Information
http://mathoverflow.net/questions/4246/why-is-milnor-k-theory-not-ad-hoc
http://mathoverflow.net/questions/9321/does-milnor-k-theory-arise-from-waldhausen-k-theory
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