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arXiv · 2403.04271

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

Nicola Nesa
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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 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.

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Nicola Nesa. 2024-03-07. Ranks of 1-motives as dimensions of Ext$^1$ vector spaces. https://arxiv.org/abs/2403.04271

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