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arXiv · 2201.08203

On the rank of Leopoldt's and Gross's regulator maps

Alexandre Maksoud
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Abstract

We generalize Waldschmidt's bound for Leopoldt's defect and prove a similar bound for Gross's defect for an arbitrary extension of number fields. As an application, we prove new cases of Gross's finiteness conjecture (also known as the Gross-Kuz'min conjecture) beyond the classical abelian case, and we show that Gross's $p$-adic regulator has at least half of the conjectured rank. We also describe and compute non-cyclotomic analogues of Gross's defect.

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Alexandre Maksoud. 2022-01-20. On the rank of Leopoldt's and Gross's regulator maps. https://doi.org/10.4171/dm/935

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