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N-dimensional rings with an isolated singular point having nonzero K-N. (English) Zbl 0634.14006

Let k be field and \(S_ d(k)\) the class of normal d-dimensional affine k-algebras whose underlying variety has a single singular point. The author constructs for any given k and \(d\geq 2\), \((1)\quad a\) k-algebra \(A\in S_ d(k)\) with \(K_{-d}(A)\neq 0\); \((2)\quad a\) k-algebra \(A\in S_ d(k)\) with \(NK_{-(d-1)}(A)\neq 0.\)
The first construction gives counter-examples to a conjecture of C. Weibel.
Reviewer: G.Dzhanelidze

MSC:

14C35 Applications of methods of algebraic \(K\)-theory in algebraic geometry
13D15 Grothendieck groups, \(K\)-theory and commutative rings
18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
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References:

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