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 …

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

Our main theorem describes the degree 0 cohomology of Igusa varieties in terms of one-
dimensional automorphic representations in the setup of mod p Hodge-type Shimura …

We give a new construction of p-adic overconvergent Hilbert modular forms by using
Scholze's perfectoid Shimura varieties at infinite level and the Hodge–Tate period map. The …

We give a new construction of $ p $-adic overconvergent Hilbert modular forms by using
Scholze's perfectoid Shimura varieties at infinite level and the Hodge--Tate period map. The …

We give an explicit description of the matrix associated to the Up operator acting on spaces
of overconvergent Hilbert modular forms over totally real fields. Using this, we compute …

We define formal vector bundles with marked sections on Hilbert modular schemes and we
show how to use them to construct modular sheaves with an integrable meromorphic …

We prove a perfectoid tilting isomorphism that describes the Hecke module of
overconvergent t-adic modular forms of Andreatta–Iovita–Pilloni at the boundary of weight …

Let $ L $ be a totally real field, and $ p $ be a rational prime that is unramified in $ L $. We
construct overconvergent families of classes of relative de Rham cohomology of the …

We use the theory of trianguline-modules over pseudorigid spaces to prove a modularity
lifting theorem for certain Galois representations which are trianguline at p, including those …