On the K-theory of local fields.(English)Zbl 0548.12009
The author completes his proof of the Lichtenbaum conjecture on the algebraic K-theory of an algebraically closed field. In [Invent. Math. 73, 241-245 (1983;Zbl 0514.18008)] he showed that it suffices to take one field of each characteristic. Here, by considering local rings, he shows that one needs only one field altogether. He computes the K-theory of the complex numbers (also of the real numbers), and so makes the proof independent of computations for fields of finite characteristic.
Reviewer: R.Steiner
MSC:
| 11S70 | \(K\)-theory of local fields |
| 18F25 | Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects) |
| 13D15 | Grothendieck groups, \(K\)-theory and commutative rings |
Keywords:
Henselian valuation rings;K-theory of local fields;K-theory of algebraically closed fields;Lichtenbaum conjectureCitations:
Zbl 0514.18008Cite
Full Text:DOI
References:
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