2007/09/26 by I. Panin, Ivan Panin, K. Pimenov +6
Mathematics · #14F05 #55N22 #55P43 #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 #math.AG #math.AT #msc:14F05 #msc:55N22 #msc:55P43
paper · pdf · doi:10.48550/arxiv.0709.4116
LaTeX, 14 pages, uses XY-pic
arxiv created 2007/09/26 · openalex publication_date 2007/09/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An algebraic version of a theorem due to Quillen is proved. More precisely, for a ground field k we consider the motivic stable homotopy category SH(k) of P1-spectra equipped with the symmetric monoidal structure described in arXiv:0709.3905v1 [math.AG]. The algebraic cobordism P1-spectrum MGL is considered as a commutative monoid equipped with a canonical orientation. For a commutative monoid E in the category SH(k) we identify the set of monoid homomorphisms from MGL to E in the motivic stable homotopy category with the set of all orientations of E. This result was stated originally in a slightly different form by G. Vezzosi in arXiv:math/0004050v2 [math.AG].