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Results tagged with algebraic-k-theory
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user 100
16
votes
Why is Milnor K-theory not ad hoc?
To help answer Question 1, Milnor proved a local-global theorem for Witt rings of global fields. Recall that The Grothendieck-Witt ring $\widehat{W}(k)$ of a field $k$ is the ring obtained by starting …
- 5,062
10
votes
K(F_1) = sphere spectrum?
Here is another heuristic, related to what Randal-Williams said above. The sphere spectrum is the unit object in nice categories of spectra. That is, ring spectra are algebras over the sphere spectrum …
- 5,062
21
votes
Motivation for algebraic K-theory?
As a particular application of algebraic K-theory, let me mention the intersection product on regular schemes. Let X be a regular scheme over spec Z. Then, one can use the Quillen spectral sequence an …
3
votes
K theory long exact sequence
You can combine Adeel Khan's answer with Proposition 6.9 of my paper with David Gepner to prove that there are these kinds of localization sequences in a great deal of generality. (Note that our propo …
- 5,062