Geometry of the eigencurve at CM points and trivial zeros of Katz \(p\)-adic \(L\)-functions

DOI10.1016/j.aim.2021.107724zbMath1483.11085arXiv1907.09422OpenAlexW3158447841MaRDI QIDQ2237359

Mladen Dimitrov, Adel Betina

Publication date: 27 October 2021

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.09422

zbMATH Keywords

deformations of Galois representationseigencurveweight one modular formsKatz \(p\)-adic \(L\)-functions

Mathematics Subject Classification ID

Congruences for modular and (p)-adic modular forms (11F33) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Galois representations (11F80) Iwasawa theory (11R23)

Related Items (9)

On Siegel eigenvarieties at Saito-Kurokawa points ⋮ ARITHMETIC OFp‐IRREGULAR MODULAR FORMS: FAMILIES ANDp‐ADICL‐FUNCTIONS ⋮ On extra zeros of 𝑝-adic Rankin–Selberg 𝐿-functions ⋮ Derivatives of Beilinson-Flach classes, Gross-Stark formulas and a \(p\)-adic Harris-Venkatesh conjecture ⋮ On the rank of Leopoldt's and Gross's regulator maps ⋮ The derivative formula of \(p\)-adic \(L\)-functions for imaginary quadratic fields at trivial zeros ⋮ \(\mathscr{L}\)-invariants of Artin motives ⋮ A geometric view on Iwasawa theory ⋮ On the failure of Gorensteinness at weight 1 Eisenstein points of the eigencurve

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