2014/11/24 by Andreas Rosenschon, V. Srinivas · 13 citations
Mathematics · #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #Advanced Algebra and Geometry #Motivic cohomology #Mathematics #Cohomology #De Rham cohomology #Group cohomology #Pure mathematics #Čech cohomology #Equivariant cohomology #Hodge conjecture #Algebra over a field #Quantum cohomology #Étale cohomology #Cup product #Algebraic cycle #Interpretation (philosophy) #Algebraic number #Hodge theory #Mathematical analysis #Computer science
paper · doi:10.1017/s1474748014000401
published in Journal of the Institute of Mathematics of Jussieu 15(3), 511-537 (Cambridge University Press)
openalex publication_date 2014/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
We consider étale motivic or Lichtenbaum cohomology and its relation to algebraic cycles. We give an geometric interpretation of Lichtenbaum cohomology and use it to show that the usual integral cycle maps extend to maps on integral Lichtenbaum cohomology. We also show that Lichtenbaum cohomology, in contrast to the usual motivic cohomology, compares well with integral cohomology theories. For example, we formulate integral étale versions of the Hodge and the Tate conjecture, and show that these are equivalent to the usual rational conjectures.