Reciprocity laws for balanced diagonal classes

M Bertolini, MA Seveso, R Venerucci - Astérisque, 2022 - smf.emath.fr
This article constructs a 3-variable balanced diagonal class κ (f, g, h) in the cohomology of
the Galois representation associated to a self-dual triple (f, g, h) of p-adic Hida families. Its …

Higher Hida theory and p-adic L-functions for

D Loeffler, V Pilloni, C Skinner… - Duke Mathematical …, 2021 - projecteuclid.org
We use the “higher Hida theory” recently introduced by the second author to p-adically
interpolate periods of nonholomorphic automorphic forms for GSp 4, contributing to coherent …

Heegner points and Beilinson–Kato elements: a conjecture of Perrin-Riou

M Bertolini, H Darmon, R Venerucci - Advances in Mathematics, 2022 - Elsevier
Heegner points and Beilinson–Kato elements: A conjecture of Perrin-Riou - ScienceDirect
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Zeta elements for elliptic curves and applications

A Burungale, C Skinner, Y Tian, X Wan - arXiv preprint arXiv:2409.01350, 2024 - arxiv.org
Let $ E $ be an elliptic curve defined over $\mathbb {Q} $ with conductor $ N $ and $ p\nmid
2N $ a prime. Let $ L $ be an imaginary quadratic field with $ p $ split. We prove the …

p-adic interpolation of Gauss--Manin connections on nearly overconvergent modular forms and p-adic L-functions

A Graham, V Pilloni, JR Jacinto - arXiv preprint arXiv:2311.14438, 2023 - arxiv.org
In this paper, we give a new geometric definition of nearly overconvergent modular forms
and $ p $-adically interpolate the Gauss-Manin connection on this space. This can be seen …

Balanced diagonal classes and rational points on elliptic curves

M Bertolini, MA Seveso, R Venerucci - Astérisque, 2022 - smf.emath.fr
Let A be an elliptic curve over the rationals with multiplicative reduction at a prime p, and let
K be a quadratic field in which p is inert. Under a generalized Heegner assumption, our …

Nearly overconvergent Siegel modular forms

Z Liu - Annales de l'Institut Fourier, 2019 - numdam.org
Shimura developed his theory of nearly holomorphic forms in his study on the algebraicity of
special L-values and Klingen Eisenstein series [42, 45]. With the goal of combining this …

Heegner points in Coleman families

D Jetchev, D Loeffler, SL Zerbes - Proceedings of the London …, 2021 - Wiley Online Library
Heegner points in Coleman families - Jetchev - 2021 - Proceedings of the London
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-adic Gross-Zagier formula at critical slope and a conjecture of Perrin-Riou

K Büyükboduk, R Pollack, S Sasaki - arXiv preprint arXiv:1811.08216, 2018 - arxiv.org
Let $ p $ be an odd prime. Given an imaginary quadratic field $ K=\mathbb {Q}(\sqrt {-D_K})
$ where $ p $ splits with $ D_K> 3$, and a $ p $-ordinary newform $ f\in S_k (\Gamma_0 …

A note on p-adic Rankin–Selberg L-functions

D Loeffler - Canadian Mathematical Bulletin, 2018 - cambridge.org
A Note on p-adic Rankin–Selberg L-functions Page 1 Canad. Math. Bull. Vol. (), pp. – http://dx.doi.org/.
/CMB--©Canadian Mathematical Society A Note on p-adic Rankin–Selberg L-functions David …