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On generalized Iwasawa main conjectures and p-adic Stark conjectures for Artin motives
Maksoud, Alexandre
2021
 

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Keywords :
Number theory; Iwasawa theory
Abstract :
[en] We continue the study of Selmer groups associated with an Artin representation endowed with a p-stabilization which was initiated in arXiv:1811.05368. We formulate a main conjecture and an extra zeros conjecture at all unramified odd primes p, which are shown to imply the p-part of the Tamagawa number conjecture for Artin motives at s=0. We also relate our new conjectures with various cyclotomic Iwasawa main conjectures and p-adic Stark conjectures that appear in the literature. In particular, they provide a natural interpretation for recent conjectures on p-adic L-functions attached to (the adjoint of) a weight one modular form. In the case of monomial representations, we prove that our conjectures are essentially equivalent to some newly introduced Iwasawa-theoretic conjectures for Rubin-Stark elements.
Disciplines :
Mathematics
Author, co-author :
Maksoud, Alexandre ;  University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
Language :
English
Title :
On generalized Iwasawa main conjectures and p-adic Stark conjectures for Artin motives
Publication date :
2021
Number of pages :
43
FnR Project :
FNR12589973 - Galois Representations, Automorphic Forms And Their L-functions, 2018 (01/02/2019-31/08/2024) - Gabor Wiese
Funders :
FNR - Fonds National de la Recherche [LU]
Commentary :
This research is supported by the Luxembourg National Research Fund, Luxembourg, INTER/ANR/18/12589973 GALF.
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since 12 March 2021

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