Geodesic
On the rank of Leopoldt’s and Gross’s regulator maps
Documenta mathematica, Tome 28 (2023) no. 6, pp. 1441-1471

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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.
DOI : 10.4171/dm/935
Classification : 11R27, 11R23
Mots-clés : Leopoldt conjecture, Gross--Kuz'min conjecture, p-adic transcendence theory, Iwasawa theory 
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Alexandre Maksoud. On the rank of Leopoldt’s and Gross’s regulator maps. Documenta mathematica, Tome 28 (2023) no. 6, pp. 1441-1471. doi: 10.4171/dm/935

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