Talk:Milnor K-theory

Latest comment: 3 years ago by Kaptain-k-theory in topic Motivic steenrod algebra

"Milnor ring" (an alternative name) redirects here. BTotaro (talk) 17:40, 4 November 2015 (UTC)Reply

Article improvements

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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

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  • graded commutative ring structure
  • 1.2 and 1.3

computations

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  • example 1.5 and implications
  • example 1.6 with generators, also include   from section 2
  •   for   can be deduced from later methods

structure results

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  • 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

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  • 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

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  • theorem 1.4 for arithmetic
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Wundzer (talk) 17:15, 22 January 2021 (UTC)Reply

Higher local class field theory

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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)Reply

Motivic steenrod algebra

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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

Kaptain-k-theory (talk) 18:19, 28 April 2021 (UTC)Reply