Introduction to the Category of Derived Motivic Spectra

2023/03/16 by Renaud Gauthier, Gauthier, Renaud
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications

paper · pdf · doi:10.48550/arxiv.2303.09537

Abstract

We formalize an abstraction of Grothendieck's philosophy of motives and construct a category of derived motivic spectra in the Segal category ℝ \underlineHom ((dSt_k)^op_/F, Top) (dSt_k the Segal category of derived stacks on sk-Alg, Top = L Set_Δ the Segal category of simplicial sets), thereby providing a starting point for a construction of a stable motivic homotopy category in the Segal setting.

Related

• Galois reconstruction of Artin-Tate ℝ-motivic spectra
• Group schemes and motivic spectra
• Motivic Landweber Exactness
• Motivic Homotopical Galois Extensions
• Motivic homotopy theory and stable homotopy groups