tale descent for hochschild and cyclic homology Academic Article uri icon

abstract

  • If B is an tale extension of a k-algebra A, we prove for Hochschild homology that HH *(B)HH*(A)AB. For Galois descent with group G there is a similar result for cyclic homology:HC *HC*(B)G if {Mathematical expression}. In the process of proving these results we give a localization result for Hochschild homology without any flatness assumption. We then extend the definition of Hochschild homology to all schemes and show that Hochschild homology satisfies cohomological descent for the Zariski, Nisnevich and tale topologies. We extend the definition of cyclic homology to finite-dimensional noetherian schemes and show that cyclic homology satisfies cohomological descent for the Zariski and Nisnevich topologies, as well as for the tale topology over Q. Finally we apply these results to complete the computation of the algebraic K-theory of seminormal curves in characteristic zero. 1991 Birkhuser Verlag.

published proceedings

  • Commentarii Mathematici Helvetici

author list (cited authors)

  • Weibel, C. A., & Geller, S. C.

citation count

  • 36

complete list of authors

  • Weibel, Charles A||Geller, Susan C

publication date

  • December 1991