Perfection in motivic homotopy theory

Abstract

We prove a topological invariance statement for the Morel-Voevodsky motivic homotopy category, up to inverting exponential characteristics of residue fields. This implies in particular that SH[1/p] of characteristic p>0 schemes is invariant under passing to perfections. Among other applications we prove Grothendieck-Verdier duality in this context.

10 pages. v3: minor revisions; to appear in Proceedings of the LMS

References in corpus (9)

• Triangulated categories of mixed motives
• A quadratic refinement of the Grothendieck-Lefschetz-Verdier trace formula
• Étale motives
• Fundamental classes in motivic homotopy theory
• Descente par éclatements en K-théorie invariante par homotopie
• On the Conservativity of the Functor Assigning to a Motivic Spectrum its Motive
• $K$-theory of valuation rings
• Algebraic elliptic cohomology theory and flops, I
• Dimensional homotopy t-structure in motivic homotopy theory

Cited by in corpus (14)

• Fundamental classes in motivic homotopy theory
• The six-functor formalism for rigid analytic motives
• On Modules Over Motivic Ring Spectra
• On the rational motivic homotopy category
• The motivic Satake equivalence
• Künneth formulas for motives and additivity of traces
• A characterization of finite étale morphisms in tensor triangular geometry
• Tate motives on Witt vector affine flag varieties
• A better comparison of cdh- and ldh-cohomologies
• The Motivic Segal-Becker Theorem
• On the ${\mathbb{A}}^1$-Euler characteristic of the variety of maximal tori in a reductive group
• Power structures on the Grothendieck--Witt ring and the motivic Euler characteristic
• Trace maps in motivic homotopy and local terms
• Trace formalism for motivic cohomology