March 7, 2024Open Access

Ranks of 1-motives as dimensions of Ext¹ vector spaces

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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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Nicola Nesa (Thu,) studied this question.

synapsesocial.com/papers/68e7567db6db6435876cdd60 https://doi.org/https://doi.org/10.48550/arxiv.2403.04271

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