Talk:Milnor K-theory
![]() | This article is rated Start-class on Wikipedia's content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
|
"Milnor ring" (an alternative name) redirects here. BTotaro (talk) 17:40, 4 November 2015 (UTC)
Article improvements
[edit]There are quite a few useful results from Milnor's original paper "Algebraic K-theory and Quadratic forms" which should be included in this article for a better understanding of Milnor K-theory.
structure of K-theory ring
[edit]- graded commutative ring structure
- 1.2 and 1.3
computations
[edit]- example 1.5 and implications
- example 1.6 with generators, also include from section 2
- for can be deduced from later methods
structure results
[edit]- example 1.7 gives partial computation of local fields : they are all divisible, moreover, using the same argument as 1.5 this gives all milnor K-groups
theorems
[edit]- theorem 2.3 (give exact sequence for Q(t), R(t), C(t) (or any algebraically closed field), showing the structure)
- C(t_1), C(t_1)(t_2), C(t_1)(t_2)(t_3), ...
- lemma 6.2 -> relation with Galois cohomology (refined further later on Bloch-Kato)
- A.2
Applications section
[edit]- theorem 1.4 for arithmetic
Other articles
[edit]- Also, mention Voevodsky's article on motivic cohomology (corollary 7.5 on page 97) https://www.math.ias.edu/vladimir/sites/math.ias.edu.vladimir/files/motivic_cohomology_with_Z2_coefficients_published.pdf
- Give motivic sheaves representing Milnor K-theory https://arxiv.org/abs/math/0107109
- Relate to motivic cohomology, higher chow groups, and higher algebraic K-theory, this shows Milnor K-theory is part of higher algebraic K-theory
Wundzer (talk) 17:15, 22 January 2021 (UTC)
Higher local class field theory
[edit]This article should mention the main theorem of local class field theory. The statement can be found in
and
contains other useful pdfs. Also,
contains useful stuff on Milnor K-theory, starting on page 292 of the pdf.
- Differential forms and Milnor K-theory
Kaptain-k-theory (talk) 20:40, 14 April 2021 (UTC)
Motivic steenrod algebra
[edit]Should discuss the relation between motivic cohomology and Milnor K-theory. In addition, discuss the various results about the motivic steenrod algebra and motivic eilenberg-maclane spaces. Some resources include