Ogus realization of 1-motives

TL;DR

This paper establishes that the Ogus realization of 1-motives over a number field is a fully faithful functor, using an algebraicity theorem to enhance the de Rham realization with an enriched structure.

Contribution

It proves the full faithfulness of the Ogus realization functor for 1-motives, extending Ogus's framework with algebraicity results by Bost.

Findings

Ogus realization is a fully faithful functor

Enriched de Rham structure over number fields

Application of Bost's algebraicity theorem

Abstract

After introducing the Ogus realization of 1-motives we prove that it is a fully faithful functor. More precisely, following a framework introduced by Ogus, considering an enriched structure on the de Rham realization of 1-motives over a number field, we show that it yields a full functor by making use of an algebraicity theorem of Bost.