  We reformulate the ranks that appear in the dimension formula for the linear
space of periods of a 1-motive established by Huber and W\"ustholz 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.
