18 citations · 108 across the 18 of their papers we have counts for
19 papers
On the variation of slopes over moduli stacks of Galois representations
John Bergdall, Robert Pollack
We determine how p-adic slopes of modular forms vary as their associated Galois representations modulo p vary over moduli of Galois representations. As a consequence, we show that…
New phenomena arising from L-invariants of modular forms
John Bergdall, Robert Pollack
This article explains how to practically compute L-invariants of p-new eigenforms using p-adic L-series and exceptional zero phenomena. As proof of the utility, we compiled a data…
Huber rings and valuation spectra
John Bergdall
These notes expand a four-hour lecture course given in Heidelberg in March 2023, as part of the "Spring School on non-Archimedean Geometry and Eigenvarieties". They are designed fo…
Slopes of modular forms and reducible Galois representations: an oversight in the ghost conjecture
John Bergdall, Robert Pollack
The ghost conjecture, formulated by this article's authors, predicts the list of p-adic valuations of the non-zero p-th eigenvalues ("slopes") for overconvergent p-adic modular eig…
A -adic adjoint -function and the ramification locus of the Hilbert modular eigenvariety
Baskar Balasubramanyam, John Bergdall, Matteo Longo
Let be a totally real field and the middle-degree eigenvariety for Hilbert modular forms over , constructed by Bergdall--Hansen. We study the ramification locu…
Reductions of -dimensional semi-stable representations with large -invariant
John Bergdall, Brandon Levin, Tong Liu
We determine reductions of 2-dimensional, irreducible, semi-stable, and non-crystalline representations of with Hodge--Tate weigh…
Reductions of some two-dimensional crystalline representations via Kisin modules
John Bergdall, Brandon Levin
We determine rational Kisin modules associated with two-dimensional, irreducible, crystalline representations of of Hodge-Tate…
Smoothness of definite unitary eigenvarieties at critical points
John Bergdall
We compute an upper bound for the dimension of the tangent spaces at classical points of certain eigenvarieties associated with definite unitary groups, especially including the so…
On -adic -functions for Hilbert modular forms
John Bergdall, David Hansen
We construct -adic -functions associated with -refined cohomological cuspidal Hilbert modular forms over any totally real field under a mild hypothesis. Our construction i…
Slopes of modular forms and the ghost conjecture, II
John Bergdall, Robert Pollack
In a previous article, we constructed an entire power series over -adic weight space (the 'ghost series') and conjectured, in the -regular case, that this series encodes…
Upper bounds for constant slope -adic families of modular forms
John Bergdall
We study -adic families of eigenforms for which the -th Hecke eigenvalue has constant -adic valuation ("constant slope families"). We prove two separate upper bounds…
Slopes of modular forms and the ghost conjecture
John Bergdall, Robert Pollack
We formulate a conjecture on slopes of overconvergent p-adic cuspforms of any p-adic weight in the Gamma_0(N)-regular case. This conjecture unifies a conjecture of Buzzard on class…
A remark on non-integral p-adic slopes for modular forms
John Bergdall, Robert Pollack
We give a sufficient condition, namely "Buzzard irregularity", for there to exist a cuspidal eigenform which does not have integral p-adic slope.
Slopes of modular forms and the ghost conjecture (unabridged version)
John Bergdall, Robert Pollack
We formulate a conjecture on slopes of overconvergent p-adic cuspforms of any p-adic weight in the Gamma_0(N)-regular case. This conjecture unifies a conjecture of Buzzard on class…
Arithmetic properties of Fredholm series for p-adic modular forms
John Bergdall, Robert Pollack
We study the relationship between recent conjectures on slopes of overconvergent p-adic modular forms "near the boundary" of p-adic weight space. We also prove in tame level 1 that…
An adjunction formula for the Emerton-Jacquet functor
John Bergdall, Przemyslaw Chojecki
The Emerton-Jacquet functor is a tool for studying locally analytic representations of p-adic Lie groups. It provides a way to access the theory of p-adic automorphic forms. Here w…
Paraboline variation of -adic families of -modules
John Bergdall
We study the -adic variation of triangulations over -adic families of -modules. In particular, we study certain canonical sub-filtrations of the pointwise triangulatio…
Ordinary representations and companion points for U(3) in the indecomposable case
John Bergdall, Przemyslaw Chojecki
We prove that certain p-adic Banach representations, associated to local ordinary Galois representations, constructed by Breuil and Herzig appears in the completed cohomology of a…
Ordinary Modular Forms and Companion Points on the Eigencurve
John Bergdall
We give a new proof of a result due to Breuil and Emerton which relates the splitting behavior at p of the p-adic Galois representation attached to a p-ordinary modular form to the…