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Lubin–Tate theory and overconvergent Hilbert modular forms of low weight
Let K be a finite extension of ℚ p and let Γ be the Galois group of the cyclotomic extension of K . Fontaine’s theory gives a classification of p -adic...
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Congruences between modular forms
We survey the connections between modular forms and representations of Galois groups that are predicted by the Langlands programme. We focus in...
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Overconvergent Eichler-Shimura isomorphisms for unitary Shimura curves over totally real fields
We compare two different cohomology groups on unitary Shimura curves over totally real number fields; these groups are used in the construction of p -a...
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Eisenstein series, p-adic modular functions, and overconvergence, II
Let p be a prime number. Continuing and extending our previous paper with the same title, we prove explicit rates of overconvergence for modular...
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Spectral halo for Hilbert modular forms
Let F be a totally real field and p be an odd prime which splits completely in F . We prove that the eigenvariety associated to a definite quaternion...
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The Eigencurve of Modular Symbols
Stevens’s overconvergent modular symbols can replace Coleman’s overconvergent modular forms in the construction of the eigencurve. We give in Sect....
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Abelian surfaces over totally real fields are potentially modular
We show that abelian surfaces (and consequently curves of genus 2) over totally real fields are potentially modular. As a consequence, we obtain the...
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p-Adic GKZ hypergeometric complex
To a torus action on a complex vector space, Gelfand, Kapranov and Zelevinsky introduce a system of differential equations, which are now called the...
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A formal model of Coleman families and applications to Iwasawa invariants
For a given Coleman family of modular forms, we construct a formal model and prove the existence of a family of Galois representations associated to...
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p-Adic L-Functions on the Eigencurve
In Chap. 5 , we defined, using the method of Manin, Višik and Amice-Velu as reinterpreted by...
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Rigid Analytic Modular Symbols and p-Adic L-functions
In all this chapter we fix an arbitrary number p.
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Le Système d’Euler de Kato en Famillie (II)
This article is the second article on the generalization of Kato’s Euler system. The main subject of this article is to construct a family of Kato’s...
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Introduction
The aim of this book is to give a gentle but complete introduction to the two interrelated theory of p-adic families of modular forms and of p-adic...
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A p-adic interpolation of generalized Heegner cycles and integral Perrin-Riou twist I
In this paper, we develop an integral refinement of the Perrin-Riou theory of exponential maps. We also formulate the Perrin-Riou theory for...
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Computational Number Theory, Past, Present, and Future
A survey of computational number theory viewed through the prism of my own experience and the Pari/GP software.