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Extensions of filtered Ogus structures

Bruno Chiarellotto, Nicola Mazzari

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.

Extensions of filtered Ogus structures

Abstract

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

Paper Structure

This paper contains 8 sections, 4 theorems, 24 equations.

Table of Contents

  1. Introduction
  2. Notations and conventions
  3. The categories
  4. The Ogus category
  5. Weights
  6. The filtered Ogus category
  7. Internal Hom
  8. Ext computation

Key Result

Lemma 2.1

The filtered Ogus category $\mathbf{FOg}(K)$ is a $\mathbb{Q}$-linear abelian category, and the forgetful functor is fully faithful.

Theorems & Definitions (10)

  • Lemma 2.1: ABVB16, Lemma 1.3.2
  • Lemma 3.1
  • proof
  • Proposition 3.2
  • proof
  • Remark 3.3
  • Proposition 3.4
  • proof
  • Remark 3.5
  • Remark 3.6