The filtered Ogus realisation of motives

TL;DR

This paper constructs a filtered Ogus realization for Voevodsky motives over a number field, extending previous functors and demonstrating the Tate conjecture analogue for K3 surfaces.

Contribution

It introduces a new filtered Ogus realization for Voevodsky motives, expanding the functorial framework and applications in algebraic geometry.

Findings

The Ogus realization extends to Voevodsky motives over number fields.

The Tate conjecture analogue is verified for K3 surfaces.

Provides a new tool for studying motives and their realizations.

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.