Equivariant semi-topological invariants, Atiyah's kr-theory, and real algebraic cycles

Jeremiah Heller, Mircea Voineagu

Research output: Contribution to journalArticle

Abstract

We establish an Atiyah-Hirzebruch type spectral sequence relating real morphic cohomology and real semi-topological K-theory and prove it to be compatible with the Atiyah-Hirzebruch spectral sequence relating Bredon cohomology and Atiyah's KR-theory constructed by Dugger. An equivariant and a real version of Suslin's conjecture on morphic cohomology are formulated, proved to come from the complex version of Suslin conjecture and verified for certain real varieties. In conjunction with the spectral sequences constructed here, this allows the computation of the real semi-topological K-theory of some real varieties. As another application of this spectral sequence we give an alternate proof of the Lichtenbaum-Quillen conjecture over R, extending an earlier proof of Karoubi and Weibel.

Original languageEnglish (US)
Pages (from-to)6565-6603
Number of pages39
JournalTransactions of the American Mathematical Society
Volume364
Issue number12
DOIs
StatePublished - 2012

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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