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


11S70 \(K\)-theory of local fields
18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
13D15 Grothendieck groups, \(K\)-theory and commutative rings


Zbl 0514.18008
Full Text: DOI


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