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 …

Let p be a positive prime integer. We construct p-adic families of de Rham cohomology
classes and therefore p-adic families of nearly overconvergent elliptic modular forms. As an …

Abstract Recently, Andreatta, Iovita and Pilloni constructed spaces of overconvergent
modular forms in characteristic p, together with a natural extension of the Coleman–Mazur …

We formulate a local analogue of the ghost conjecture of Bergdall and Pollack, which
essentially relies purely on the representation theory of GL 2 (Q p). We further study the …

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 …

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 …

We prove an analogue of Scholze's Primitive Comparison Theorem for proper rigid spaces
over an algebraically closed non-archimedean field $ K $ of characteristic $ p $. This implies …

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 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 …