2012/11/30 by Parker E. Lowrey, Parker Lowrey, Timo Schürg
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic number #Cobordism #Cohomology #Discrete mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematics #Morphism #Pure mathematics #math.AG #math.AT #math.KT #msc:14C40 #msc:14F43 #msc:55N22
paper · pdf · doi:10.1017/s1474748014000334
published as J. Inst. Math. Jussieu 15 (2016) 407-443 · Comments welcome. 35 pages; v2: Changes following referee's suggestions;to appear in JIMJ
arxiv created 2014/10/05 · openalex publication_date 2014/10/30 · arxiv updated 2019/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We construct a cohomology theory using quasi-smooth derived schemes as generators and an analog of the bordism relation using derived fiber products as relations. This theory has pull-backs along all morphisms between smooth schemes independent of any characteristic assumptions. We prove that, in characteristic zero, the resulting theory agrees with algebraic cobordism as defined by Levine and Morel. We thus obtain a new set of generators and relations for algebraic cobordism.