2010/12/01 by Andrew Salch, A. Salch, Salch, A. · 1 citation
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #math.AT
paper · pdf · doi:10.48550/arxiv.1012.0110
arxiv created 2010/12/01 · openalex publication_date 2010/12/01 · arxiv updated 2010/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define the derived category of a concrete category in a way which extends the usual definition of the derived category of a ring, and we prove that the bounded-below derived category of \Spec \mathbbM0 (an approximation, used by e.g. Connes and Consani, to "\Spec of the field with one element") is the stable homotopy category of connective spectra. We also describe some basic features of Grothendieck duality for the map from \Spec ℤ to \Spec \mathbbM0, or, what comes to the same thing, the map from \Spec ℤ to \Spec of the sphere spectrum; these basic features include a computation of the homology of the dualizing complex f^!(S) of abelian groups associated to the sphere spectrum.