On locally analytic vectors of the completed cohomology of modular curves
L Pan - Forum of Mathematics, Pi, 2022 - cambridge.org
We study the locally analytic vectors in the completed cohomology of modular curves and
determine the eigenvectors of a rational Borel subalgebra of. As applications, we prove a …
determine the eigenvectors of a rational Borel subalgebra of. As applications, we prove a …
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 …
and $ p $-adically interpolate the Gauss-Manin connection on this space. This can be seen …
Geometric Sen theory over rigid analytic spaces
JE Camargo - arXiv preprint arXiv:2205.02016, 2022 - arxiv.org
arXiv:2205.02016v2 [math.NT] 31 Aug 2022 Page 1 arXiv:2205.02016v2 [math.NT] 31 Aug 2022
GEOMETRIC SEN THEORY OVER RIGID ANALYTIC SPACES JUAN ESTEBAN RODRÍGUEZ …
GEOMETRIC SEN THEORY OVER RIGID ANALYTIC SPACES JUAN ESTEBAN RODRÍGUEZ …
On the Birch-Swinnerton-Dyer conjecture for modular abelian surfaces
D Loeffler, SL Zerbes - arXiv preprint arXiv:2110.13102, 2021 - arxiv.org
Let $ A $ be a modular abelian surface over $ Q $ which either has trivial geometric
endomorphism ring, or arises as the restriction of scalars of an elliptic curve over an …
endomorphism ring, or arises as the restriction of scalars of an elliptic curve over an …
Construction of eigenvarieties
J Newton - Non-Archimedean geometry and eigenvarieties, 2024 - ems.press
These are notes based on four lectures that were given at the Heidelberg spring school on
non-archimedean geometry and eigenvarieties. None of the contents are original work. Our …
non-archimedean geometry and eigenvarieties. None of the contents are original work. Our …
The cohomology of Shimura varieties with torsion coefficients
A Caraiani - Proc. Int. Cong. Math, 2022 - content.ems.press
In this article, we survey recent work on some vanishing conjectures for the cohomology of
Shimura varieties with torsion coefficients, under both local and global conditions. We …
Shimura varieties with torsion coefficients, under both local and global conditions. We …
The infinite fern in higher dimensions
V Hernandez, B Schraen - arXiv preprint arXiv:2210.10564, 2022 - arxiv.org
If $\bar\rho $ is an automorphic modulo $ p $ Galois representation, it is natural to wonder if
automorphic points are Zariski dense in the deformation space of $\bar\rho $. We prove new …
automorphic points are Zariski dense in the deformation space of $\bar\rho $. We prove new …
Congruence modules and the Wiles-Lenstra-Diamond numerical criterion in higher codimensions
SB Iyengar, CB Khare, J Manning - Inventiones mathematicae, 2024 - Springer
We define a congruence module\(\Psi _ {A}(M)\) associated to a surjective\(\mathcal {O}\)-
algebra morphism\(\lambda\colon A\to\mathcal {O}\), with\(\mathcal {O}\) a discrete valuation …
algebra morphism\(\lambda\colon A\to\mathcal {O}\), with\(\mathcal {O}\) a discrete valuation …
Asai-Flach classes and p-adic L-functions
G Grossi, D Loeffler, SL Zerbes - arXiv preprint arXiv:2309.07536, 2023 - arxiv.org
We prove a formula for the Bloch-Kato logarithm of the bottom class in the Asai-Flach Euler
system associated to a quadratic Hilbert modular form. We show that this can be expressed …
system associated to a quadratic Hilbert modular form. We show that this can be expressed …
Overconvergent modular forms are highest-weight vectors in the Hodge-Tate weight zero part of completed cohomology
S Howe - Forum of Mathematics, Sigma, 2021 - cambridge.org
We construct a. Under minor assumptions, we deduce a conjecture of Gouvea on the Hodge-
Tate-Sen weights of Galois representations attached to overconvergent modular forms. Our …
Tate-Sen weights of Galois representations attached to overconvergent modular forms. Our …