Charles A. Weibel

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Using hypercohomology, we can extend cyclic homology from algebras to all schemes over a ring k. By ‘extend’ we mean that the usual cyclic homology of any commutative algebra agrees with the cyclic homology of its corresponding affine scheme. The purpose of this paper is to show that there is a cyclic homology theory HC∗ of schemes over a commutative ring(More)
We relate the negative K-theory of a normal surface to a resolution of singularities. The only nonzero K-groups are K −2, which counts loops in the exceptional fiber, and K −1, which is related to the divisor class groups of the complete local rings at the singularities. We also verify two conjectures of Srinivas about K0-regularity and K−1 of a surface.(More)
In this paper we study several algebraic invariants of a real curve X: the Picard group Pic(X), the Brauer group Br(X), the K-theory matrix invariant SK1(X), the étale cohomology groups H(X,Z/2), and the sheaves H associated to these cohomology groups. We relate these to two topological invariants of the space X(R) of real points of X: the number c of(More)
If X is a smooth curve defined over the real numbers R, we show that Kn(X) is the sum of a divisible group and a finite elementary abelian 2-group when n ≥ 2. We determine the torsion subgroup of Kn(X), which is a finite sum of copies of Q/Z and Z/2, only depending on the topological invariants of X(R) and X(C), and show that (for n ≥ 2) these torsion(More)