Holmstrom Milnor K-theory

Milnor K-theory

Efrat

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Milnor K-theory

Here is something on the Vostokov symbol, a map from Milnor K-theory to Fontaine-Messing cohomology.

The Milnor-Chow homomorphism revisited, by Moritz Kerz and Stefan Mueller-Stach: http://www.math.uiuc.edu/K-theory/0767#

Levine in K-theory handbook, page 446: There is a canonical map from Milnor K-theory to Quillen K-theory, which identifies $K^M_n(F)_{\mathbb{Q}}$ with $K_n(F)^{(n)}$ (here F is a field). In fact, one has $K^M_n(F) \cong CH^n(F,n)$

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Milnor K-theory

Milnor: Introduction to algebraic K-theory (1971). Other original stuff by Milnor???

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Milnor K-theory

MathSciNet

Google Scholar

Google

arXiv: Experimental full text search

arXiv: Abstract search

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Milnor K-theory

AG (Algebraic geometry), AAG (Arithmetic algebraic geometry)

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Milnor K-theory

Kth

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Milnor K-theory

The Milnor conjecture. See for example Kahn’s Bourbaki account, reproduced in K-theory handbook, Vol 2.

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Milnor K-theory

See also Motivic cohomology

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Milnor K-theory

Chapter 7 of Gille and Szamuely (in Various folder under ALGEBRA)

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Milnor K-theory

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

http://mathoverflow.net/questions/52177/is-there-a-clean-definition-of-the-residue-map-in-milnor-k-theory

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Milnor K-theory

Akhtar

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 $k$. This implies that Milnor K-theory, if required to satisfy these axioms, cannot be extended to the category of varieties over $k$.

Kerr: A regulator formula for Milnor K-groups (2003)

Motivic interpretation of Milnor K-groups attached to Jacobian varieties, by Satoshi Mochizuki: http://www.math.uiuc.edu/K-theory/0774

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.

nLab page on Milnor K-theory