Joaquín Rodrigues Jacinto
joaquin.rodrigues-jacinto at univ-amu.fr
Welcome!
I am a Maître de Conférences at the Université Aix-Marseille. My main research areas are Algebraic Number Theory and Arithmetic Geometry. I am interested in the construction of p-adic L-functions, and in their connection to the p-adic Langlands correspondence. I also work in the study of special values of L-function framed in the setting of Deligne-Beilinson and Tate conjectures. Lately, I have been working on the applications of condensed mathematics to p-adic representation theory.
Articles and preprints
p-adic interpolation of Gauss-Manin connections on nearly overconvergent modular forms and p-adic L-functions (with A. Graham and V. Pilloni), Preprint 2023, 45 pages (arXiv:2311.14438)
An introduction to p-adic L-functions (with Chris Williams), Preprint 2023, 66 pages (arXiv:2309.15692)
Solid locally analytic representations (with J. E. Rodríguez Camargo), Preprint 2023, 51 pages. (arXiv:2305.03162)
Algebraic cycles and functorial lifts from G2 to PGSp6 (with A. Cauchi and F. Lemma), Preprint 2022, 57 pages. (arXiv:2202.09394)
Tempered currents and Deligne cohomology of Shimura varieties, with an application to GSp6 (with J. I. Burgos Gil, A. Cauchi and F. Lemma), Preprint 2022, 47 pages. (arXiv:2204.05163)
On higher regulators of Siegel varieties (with A. Cauchi and F. Lemma), Preprint 2019 (revised in 2022), 30 pages. (arXiv:1910.11207)
Solid locally analytic representations of p-adic Lie groups (with J.E. Rodríguez Camargo), Representation Theory 26 (2022), 962–1024 (arXiv:2110.11916, journal)
Norm-compatible systems of Galois cohomology classes for GSp6 (with A. Cauchi), Documenta Mathematica 25 (2020), 911-954 (arXiv:1807.06512, journal)
Arithmetic families of (φ,Γ)-modules and locally analytic representations of GL2(Qp), (with I. Gaisin) Documenta Mathematica 23 (2018), 1313-1404 (arXiv:1703.01627, journal)
La conjecture ε locale de Kato en dimension 2, Mathematische Annalen 372-3 (2018), 1277--1334 (arXiv:1702.05637, journal),
(φ,Γ)-modules de de Rham et fonctions L p-adiques, Algebra & Number Theory 12-4 (2018), 885--934 (arXiv:1702.05636, journal)
(φ,Γ)-modules de de Rham et fonctions L p-adiques, Ph.D. Thesis (link).
Teaching
2023-2024 :
Théorie algorithmique des nombres (notes)
Analyse 2
Algèbre 3
2022-2023 :
Représentations des groupes finis :
During 2023, I will be in charge for the problem sessions of a Master 1 course on linear representations of finite groups at the Université Sorbonne Paris Nord.
Cryptographie :
In 2022 I was in charge for the problem sessions of a Master 2 course on cryptography at the Université Sorbonne Paris Nord. Below you can find the problem sets (in french):
TD1., TD2, TD3, TD4, TD5, TD6.
Other writings