Extensions of filtered Ogus structures

TL;DR

This paper investigates the Ext groups in the filtered Ogus category over a number field and demonstrates that the filtered Ogus realization of mixed motives does not fully capture all morphisms.

Contribution

It provides the first computation of Ext groups in the filtered Ogus category and shows the limitations of the filtered Ogus realization for mixed motives.

Findings

Computed Ext groups in the filtered Ogus category.

Proved the filtered Ogus realization of mixed motives is not fully faithful.

Highlighted limitations in the current realization theory.

Abstract

We compute the Ext group of the (filtered) Ogus category over a number field $K$. In particular we prove that the filtered Ogus realisation of mixed motives is not fully faithful.