2023/10/24 by Ahina Nandy, Nandy, Ahina
Mathematics · #14F42 #55N22 #57R77 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2310.15721
openalex publication_date 2023/10/24 · openalex created_date 2023/10/26 · openalex updated_date 2026/07/28
Conner and Floyd determined the torsion in the special unitary bordism MSU back in the late 1960s. One of the ingredients of their work was an interpolation between MSU and unitary bordism MU. In this work, we prove an exactly similar relation between the special, and general linear algebraic cobordism MSL, and MGL in the stable motivic homotopy category over any Noetherian base scheme of finite Krull dimension. This gives a filtration of MGL in terms of MSL, and the skeletal filtration of ℙ∞. Using that, we compute the first slice of MSL over characteristic zero fields. We also compute the first line of the stable homotopy groups of MSL over fields of characteristic zero.