Milnor Ktheory

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 Ktheory 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 Ktheory, must be surjective when evaluated on the ground field . This implies that Milnor Ktheory, if required to satisfy these axioms, cannot be extended to the category of varieties over .
Kerr: A regulator formula for Milnor Kgroups (2003)
Motivic interpretation of Milnor Kgroups attached to Jacobian varieties, by Satoshi Mochizuki: K0774
MüllerStach and ElbazVincent: Milnor Ktheory of rings, higher Chow groups and applications
The Gersten conjecture for Milnor Ktheory , by Moritz Kerz
MR2034645 (2004m:19003) Cathelineau, JeanLouis(FNICELD) Projective configurations, homology of orthogonal groups, and Milnor $K$theory.
Milnor: Algebraic Ktheory and quadratic forms (1969/70)
Totaro: Milnor Ktheory is the simplest part of algebraic Ktheory (1992)
Voevodsky, Vishik, Orlov: An exact sequence for mod 2 Milnor Kth 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 Jfiltration conjecture.
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Other Information
http://mathoverflow.net/questions/4246/whyismilnorktheorynotadhoc
http://mathoverflow.net/questions/9321/doesmilnorktheoryarisefromwaldhausenktheory
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