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Cohomological dimension of Laumon 1-motives up to isogenies

N. Mazzari

Abstract

We prove that the category of Laumon 1-motives up isogenies over a field of characteristic zero is of cohomological dimension $\le 1$. As a consequence this implies the same result for the category of formal Hodge structures of level $\le 1$ (over $\mathbb{Q}$).

Cohomological dimension of Laumon 1-motives up to isogenies

Abstract

We prove that the category of Laumon 1-motives up isogenies over a field of characteristic zero is of cohomological dimension . As a consequence this implies the same result for the category of formal Hodge structures of level (over ).

Paper Structure

This paper contains 6 sections, 8 theorems, 30 equations.

Table of Contents

  1. Laumon 1-motives
  2. fppf sheaves
  3. Extensions
  4. The group of $n$-extensions
  5. A lemma on 2-fold extensions
  6. Ext of 1-motives up to isogenies

Key Result

Proposition 1.4

The category $\mathcal{M}_1^{\rm a}$ of Laumon 1-motives (over ${\mathnormal{k}}$) is an additive category with kernels and co-kernels.

Theorems & Definitions (22)

  • Definition 1.1
  • Definition 1.2
  • Remark 1.3
  • Proposition 1.4
  • proof
  • Remark 1.5
  • Remark 1.6
  • Proposition 1.7
  • proof
  • Remark 1.8
  • ...and 12 more