On Leopoldt's and Gross's defects for Artin representations

Reference : On Leopoldt's and Gross's defects for Artin representations


	Document type :	E-prints/Working papers : Already available on another site
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/49863

Title :	On Leopoldt's and Gross's defects for Artin representations
Language :	English
Author, co-author :	Maksoud, Alexandre [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
Publication date :	2022
Number of pages :	19
Peer reviewed :	No
Keywords :	[en] Leopoldt conjecture ; Gross-Kuz'min conjecture ; Iwasawa theory
Abstract :	[en] 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 the generalized Gross 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.
Funders :	Fonds National de la Recherche - FnR
Permalink :	http://hdl.handle.net/10993/49863
source URL :	https://arxiv.org/abs/2201.08203
FnR project :	FnR ; FNR12589973 > Gabor Wiese > GALF > Galois Representations, Automorphic Forms And Their L-functions > 01/02/2019 > 31/01/2023 > 2018

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