Reference : On generalized Iwasawa main conjectures and p-adic Stark conjectures for Artin motives
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Physical, chemical, mathematical & earth Sciences : Mathematics
On generalized Iwasawa main conjectures and p-adic Stark conjectures for Artin motives
Maksoud, Alexandre mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
[en] Number theory ; Iwasawa theory
[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.
Fonds National de la Recherche - FnR
Researchers ; Students
This research is supported by the Luxembourg National Research Fund, Luxembourg, INTER/ANR/18/12589973 GALF.
FnR ; FNR12589973 > Gabor Wiese > GALF > Galois Representations Automorphic Forms And Their L-functions > 01/02/2019 > 31/01/2023 > 2018

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