Examples of non-algebraic classes in the Brown–Peterson tower

2016/11/28 by Gereon Quick
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic cycle #Algebraic number #Artificial intelligence #Class (philosophy) #Cohomology #De Rham cohomology #Discrete mathematics #Equivariant cohomology #Homotopy and Cohomology in Algebraic Topology #Image (mathematics) #Mathematical analysis #Mathematics #Motivic cohomology #Pure mathematics #Tower #math.AG #math.AT

paper · pdf · doi:10.1007/s00209-018-2164-4

published as Math. Z. 293 (2019) 25-37 · 12 pages

arxiv created 2016/11/28 · openalex publication_date 2018/11/09 · arxiv updated 2020/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

For every n≥ 0, we construct classes in the Brown-Peterson cohomology BP⟨ n ⟩ of smooth projective complex algebraic varieties which are not in the image of the cycle map from the corresponding motivic Brown-Peterson cohomology. This generalizes the examples of Atiyah and Hirzebruch to all finite levels in the Brown-Peterson tower.

Citations

• Torsion algebraic cycles and complex cobordism
• Analytic cycles on complex manifolds
• A spectrum whose Zp cohomology is the algebra of reduced pth powers
• On the formal group laws of unoriented and complex cobordism theory