Effective motives with and without transfers in characteristic $p$

Abstract

We prove the equivalence between the category ${\mathbf{RigDM}}_{et}^{eff}(K,\mathbb{Q})$ of effective motives of rigid analytic varieties over a perfect complete non-archimedean field $K$ and the category ${\mathbf{RigDM}}_{Frobet}^{eff}(K,\mathbb{Q})$ which is obtained by localizing the category of motives without transfers ${\mathbf{RigDA}}_{et}^{eff}(K,\mathbb{Q})$ over purely inseparable maps. In particular, we obtain an equivalence between ${\mathbf{RigDM}}_{et}^{eff}(K,\mathbb{Q})$ and ${\mathbf{RigDA}}_{et}^{eff}(K,\mathbb{Q})$ in the characteristic $0$ case and an equivalence between ${\mathbf{DM}}_{et}^{eff}(K,\mathbb{Q})$ and ${\mathbf{DA}}_{Frobet}^{eff}(K,\mathbb{Q})$ of motives of algebraic varieties over a perfect field $K$. We also show a relative and a stable version of the main statement.

Small changes, final version. Link to published version http://www.sciencedirect.com/science/article/pii/S0001870816315122 - 21 pages

References in corpus (2)

• A motivic version of the theorem of Fontaine and Wintenberger
• Frobenius gauges and a new theory of p-torsion sheaves in characteristic p. I

Cited by in corpus (5)

• A motivic version of the theorem of Fontaine and Wintenberger
• The Monsky-Washnitzer and the overconvergent realizations
• Rigid cohomology via the tilting equivalence
• Rigidity for rigid analytic motives
• The Berkovich realization for rigid analytic motives