Ranks of 1-motives as dimensions of Ext${}^1$ vector spaces

We reformulate the ranks that appear in the dimension formula for the linear space of periods of a 1-motive established by Huber and Wüstholz in a more conceptual and categorical way, as dimensions of Ext${}^1$ vector spaces. This constitutes the first step towards rewriting the dimension formula purely in general categorical terms, rather than through definitions and computations introduced ad hoc for 1-motives.