Brown representability in \A¹-homotopy theory

2009/09/10 by Niko Naumann, N. Naumann, Naumann, N. +3
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AG #math.AT #msc:14F42 #msc:18E30

paper · pdf · doi:10.48550/arxiv.0909.1943

arxiv created 2009/09/10 · arxiv updated 2009/12/01

Abstract

We prove the following result of V. Voevodsky. If S is a finite dimensional noetherian scheme such that S=∪_α\Spec(R_α) for \em countable rings R_α, then the stable motivic homotopy category over S satisfies Brown representability.

Related

• Derived categories, resolutions, and Brown representability
• Motivic homotopy theory of group scheme actions
• The dual of Brown representability for homotopy categories of complexes
• Motivic strict ring models for K-theory
• Representability theorems, up to homotopy