2008/07/14 by Marc Levine, Levine, Marc
Mathematics · #14C25 #19E15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.AG #math.KT #msc:14C25 #msc:19E15
paper · pdf · doi:10.48550/arxiv.0807.2257
47 pages. To appear in Michigan Math. J
arxiv created 2008/07/14 · openalex publication_date 2008/07/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We examine various versions of oriented cohomology and Borel-Moore homology theories in algebraic geometry and put these two together in the setting of an "oriented duality theory", a generalization of Bloch-Ogus twisted duality theory. This combines and exends work of Panin and Mocanasu. We apply this to give a Borel-Moore homology version MGL'*,* of Voevodsky's MGL*,*-theory, and a natural map ϑ:Ω_*→ MGL'2*,*, where Ω_* is the algebraic cobordism theory defined by Levine-Morel. We conjecture that ϑ is an isomorphism and describe a program for proving this conjecture.