We construct the compatible system of l-adic representations associated to a regular
algebraic cuspidal automorphic representation of GL_n GL n over a CM (or totally real) field …

We show that abelian surfaces (and consequently curves of genus 2) over totally real fields
are potentially modular. As a consequence, we obtain the expected meromorphic …

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

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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 introduce a method for producing congruences between Hecke eigenclasses, possibly
torsion, in the coherent cohomology of automorphic vector bundles on certain good …

Higher coherent cohomology andp-adic modular forms of singular weights Page 1 HIGHER
COHERENT COHOMOLOGY AND p-ADIC MODULAR FORMS OF SINGULAR WEIGHTS V …

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 …

In this paper we prove the $\pm $-main conjecture of Iwasawa theory formulated by
Kobayashi for elliptic curves with supersingular reduction at an odd prime $ p $ such that …