The starting point for this course is Drinfeld's work [Dri80] on the global Langlands
correspondence over function fields. Fix X/Fp a smooth projective curve, with function field K …

​ This book discusses the p-adic modular forms, the eigencurve that parameterize them,
and the p-adic L-functions one can associate to them. These theories and their …

We prove that the eigencurve associated to a definite quaternion algebra over Q satisfies the
following properties, as conjectured by Coleman and Mazur as well as Buzzard and …

We give a new construction of overconvergent modular forms of arbitrary weights, defining
them in terms of functions on certain affinoid subsets of Scholze's infinite-level modular …

We study the cohomology of families of-modules with coefficients in pseudoaffinoid
algebras. We prove that they have finite cohomology, and we deduce an Euler characteristic …

Slopes of Modular Forms and the Ghost Conjecture Page 1 J. Bergdall and R. Pollack (2017)
“Slopes of Modular Forms and the Ghost Conjecture,” Slopes of Modular Forms and the Ghost …

We prove Riemann's theorems on extensions of functions over certain mixed characteristic
analytic adic spaces, first introduced by Johansson and Newton. We use these results to …

We study the basic geometry of a class of analytic adic spaces that arise in the study of the
extended (or adic) eigenvarieties constructed by Andreatta--Iovita--Pilloni, Gulotta and the …

Let K be an imaginary quadratic field. In this article, we study the eigenvariety for GL 2/K,
proving an étaleness result for the weight map at non-critical classical points and a …

We construct $ p $-adic $ L $-functions associated with $ p $-refined cohomological
cuspidal Hilbert modular forms over any totally real field under a mild hypothesis. Our …