The filtered Ogus realisation of motives

Abstract

We construct the (filtered) Ogus realisation of Voevodsky motives over a number field $K$. This realisation extends the functor defined on $1$-motives by Andreatta, Barbieri-Viale and Bertapelle. As an illustration we note that the analogue of the Tate conjecture holds for K3 surfaces.

arXiv commentfinal accepted version

References in corpus (7)

• Albanese and Picard 1-motives
• Crystalline realizations of 1-motives
• The rigid syntomic ring spectrum
• Cycle classes and the syntomic regulator
• Nori 1-motives
• Construction de courbes sur les surfaces K3 [d'après Bogomolov-Hassett-Tschinkel, Charles, Li-Liedtke, Madapusi Pera, Maulik...]
• Ogus realization of 1-motives

Cited by in corpus (2)

• The Fontaine-Ogus realisation of Laumon 1-motives
• Extensions of filtered Ogus structures