Cohomological dimension of Laumon 1-motives up to isogenies

TL;DR

This paper proves that the category of Laumon 1-motives up to isogenies over a field of characteristic zero has cohomological dimension at most 1, impacting related categories like formal Hodge structures.

Contribution

It establishes the cohomological dimension bound for Laumon 1-motives up to isogenies, a new result in the understanding of their categorical properties.

Findings

Cohomological dimension of Laumon 1-motives is ≤ 1.

Same bound applies to formal Hodge structures of level ≤ 1.

Results hold over fields of characteristic zero.

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 $\mathbb{Q}$).