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 …

Using the overconvergent cohomology modules introduced by Ash–Stevens, we construct
eigenvarieties associated with reductive groups and establish some basic geometric …

Let p be an odd prime and g≥ 2 an integer. We prove that a finite slope Siegel cuspidal
eigenform of genus g can be p-adically deformed over the g-dimensional weight space. The …

​ 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 …

arXiv:2002.06845v2 [math.NT] 11 Sep 2022 Page 1 Épijournal de Géométrie Algébrique
epiga.episciences.org Volume 6 (2022), Article Nr. 16 Higher Hida and Coleman theories on the …

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 …

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 …

Nous construisons un espace de formes surconvergentes en caractéristique p, un opérateur
compact sur cet espace, et nous montrons que la série caractéristique de cet opérateur est …

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 …

Let $ F $ be a totally real field in which $ p $ is unramified. We prove that, if a cuspidal
overconvergent Hilbert cuspidal form has small slopes under $ U_p $-operators, then it is …