Ranks of 1-motives as dimensions of Ext1 vector spaces
Abstract
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 Ext1 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.
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