Overconvergent cohomology of Hilbert modular varieties and p-adic L-functions
نویسندگان
چکیده
منابع مشابه
AUTOMORPHIC SYMBOLS, p-ADIC L-FUNCTIONS AND ORDINARY COHOMOLOGY OF HILBERT MODULAR VARIETIES
We introduce the notion of automorphic symbol generalizing the classical modular symbol and use it to attach very general p-adic L-functions to nearly ordinary Hilbert automorphic forms. Then we establish an exact control theorem for the p-adically completed cohomology of a Hilbert modular variety localized at a suitable nearly ordinary maximal ideal of the Hecke algebra. We also show its freen...
متن کاملOVERCONVERGENT MODULAR SYMBOLS AND p-ADIC L-FUNCTIONS
Cet article est exploration constructive des rapports entre les symboles modulaires classique et les symboles modulaires p-adiques surconvergents. Plus précisément, on donne une preuve constructive d’un theorème de controle (Theoreme 1.1) du deuxiéme auteur [20]; ce theoréme preuve l’existence et l’unicité des “liftings propres” des symboles propres modulaires classiques de pente non-critique. ...
متن کاملEisenstein Cohomology and p - adic L - Functions
§0. Introduction. In this paper, we define the module D̃(V ) of distributions with rational poles on a finite dimensional rational vector space a V . This is an infinite dimensional vector space over Q endowed with a natural action of the reductive group GV := Aut(V ). Indeed, this action extends to a natural action of the adelic group GV (AQ). For each prime p, we define we define the notion of...
متن کاملGALOIS REPRESENTATIONS MODULO p AND COHOMOLOGY OF HILBERT MODULAR VARIETIES
The aim of this paper is to extend some arithmetic results on elliptic modular forms to the case of Hilbert modular forms. Among these results let’s mention : − the control of the image of the Galois representation modulo p [37][35], − Hida’s congruence criterion outside an explicit set of primes p [21], − the freeness of the integral cohomology of the Hilbert modular variety over certain local...
متن کاملIwasawa theory of overconvergent modular forms, I: Critical-slope p-adic L-functions
We construct an Euler system of p-adic zeta elements over the eigencurve which interpolates Kato’s zeta elements over all classical points. Applying a big regulator map gives rise to a purely algebraic construction of a two-variable p-adic L-function over the eigencurve. As a first application of these ideas, we prove the equality of the p-adic L-functions associated with a critical-slope refin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2018
ISSN: 0373-0956,1777-5310
DOI: 10.5802/aif.3206