K-theory of cones of smooth varieties

G. Cortiñas, C. Haesemeyer, M. E. Walker, C. Weibel

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Let R be the homogeneous coordinate ring of a smooth projective variety X over a field k of characteristic 0. We calculate the κ-theory of R in terms of the geometry of the projective embedding of X. In particular, if X is a curve, then we calculate K0(R) and K1(R), and prove that K-1(R) = H1 (C, 0(n)). The formula for K0(R) involves the Zariski cohomology of twisted Kähler differentials on the variety.

Original languageEnglish (US)
Pages (from-to)13-34
Number of pages22
JournalJournal of Algebraic Geometry
Volume22
Issue number1
DOIs
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • Geometry and Topology
  • Algebra and Number Theory

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