Papers and other writings
Papers:
Théorie d'Iwasawa des motifs d'Artin et des formes modulaires de poids 1. (accepted in Annales Inst. Fourier) [arXiv]
On generalized Iwasawa main conjectures and p-adic Stark conjectures for Artin motives. (accepted in Trans. Amer. Math. Soc.) [arXiv]
On Leopoldt's and Gross's defects for Artin representations. Documenta Mathematica 28 (2023), 1441–1471
L-invariants of Artin motives. (with Mladen Dimitrov) Ann. Math. du Québec 47 (2023), 49–71
A canonical generator for congruence ideals of Hida families. (submitted) [arXiv]
Adjoint p-adic L-functions and a formula in weight one (in preparation)
PhD Thesis:
Title: Théorie d'Iwasawa des motifs d'Artin
Abstract: This thesis studies from the viewpoint of cyclotomic Iwasawa theory certain non-critical Artin motives (in the sense of Deligne), and in particular those attached to classical weight one modular forms that are regular at p. Firstly we define a Selmer group, and show that it is torsion on the corresponding Iwasawa algebra. We then compute the constant term of its caracteristic series in terms of p-adic logarithms of global units, under some mild assumptions. We also highlight a phenomenon of trivial zeros à la Mazur-Tate-Teitelbaum. Secondly we construct a p-adic L-function by deformation by means of Hida theory. Finally we formulate a Iwasawa Main Conjecture for such Artin motives. We show that it follows from the Iwasawa Main Conjecture for ordinary modular forms of weight greater than or equal to 2, and we inconditionally prove one divisibility of our Conjecture.
Defended at University of Lille on the 13/06/2019.
Keywords:
Iwasawa theory - Artin motives - p-adic L-functions - weight one modular forms - p-adic families of automorphic forms - congruence ideals - p-adic transcendence theory - p-adic Stark conjectures - Bloch-Kato conjecture - Leopoldt conjecture - Gross-Kuzmin conjecture
Websites of colleagues: