N-dimensional rings with an isolated singular point having nonzero K-N (Q1096682)

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.