Cohomological dimension of Laumon 1-motives up to isogenies
  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 $\mathbb{Q}$). 
N. Mazzari