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1. Overconvergent modular forms and the Fontaine-Mazur conjecture

   We prove a conjecture of Fontaine and Mazur on modularity of representations of G _ℚ which are potentially semi-stable at p , for representations...

   Mark Kisin in Inventiones mathematicae

   Article 10 April 2003

2. Sous-groupes canoniques et cycles évanescents p-adiques pour les variétés abéliennes

   Ahmed Abbes, Abdellah Mokrane in Publications Mathématiques de l'Institut des Hautes Études Scientifiques

   Article 01 June 2004

3. Integral structures in automorphic line bundles on the p-adic upper half plane

   Given an automorphic line bundle of weight k on the Drinfel’d upper half plane X over a local field K , we construct a GL ₂ ( K )-equivariant integral...

   Elmar Grosse-Klönne in Mathematische Annalen

   Article 17 February 2004

4. Two variable p-adic L functions attached to eigenfamilies of positive slope

   Consider a classical cusp eigenform f =∑ _{n =1} ^∞ a _n ( f ) q ⁿ of weight k ≥2 for Γ ₀ ( N ) with a Dirichlet character ψ mod N , and let L ...

   A.A. Panchishkin in Inventiones mathematicae

   Article 01 July 2003

5. Counting Solutions to Equations in Many Variables over Finite Fields

   We present a polynomial-time algorithm for computing the zeta function of a smooth projective hypersurface of degree d over a finite field of...

   Alan G. B. Lauder in Foundations of Computational Mathematics

   Article 30 January 2004

6. Computing Zeta Functions of Kummer Curves via Multiplicative Characters

   We present a practical polynomial-time algorithm for computing the zeta function of a Kummer curve over a finite field of small characteristic. Such...

   Alan G.B. Lauder in Foundations of Computational Mathematics

   Article 29 November 2002

7. Global L-functions over function fields

   Gebhard Böckle in Mathematische Annalen

   Article 01 August 2002

8. An Extension of Kedlaya’s Algorithm to Artin-Schreier Curves in Characteristic 2

   In this paper we present an extension of Kedlaya’s algorithm for computing the zeta function of an Artin-Schreier curve over a finite field...

   Jan Denef, Frederik Vercauteren in Algorithmic Number Theory

   Conference paper 2002
   

9. Pure L-Functions from Algebraic Geometry over Finite Fields

   This survey gives a concrete and intuitively self-contained introduction to the theory of pure L-functions arising from a family of algebraic...

   Daqing Wan in Finite Fields and Applications

   Conference paper 2001
   

10. A generalization of Coleman’s p-adic integration theory

    We associate to a scheme X smooth over a p -adic ring a kind of cohomology group H ⁱ _fp (X,j) . For proper X this cohomology has Poincaré duality hence...

    Amnon Besser in Inventiones mathematicae

    Article 01 November 2000

11. Canonical extensions, irregularities, and the Swan conductor

    Richard Crew in Mathematische Annalen

    Article 01 January 2000

12. Dimension variation of classical and p-adic modular forms

    A quadratic bound is obtained for a conjecture of Gouvêa-Mazur on arithmetic variation of dimensions of classical and p -adic modular forms.

    Daqing Wan in Inventiones mathematicae

    Article 01 July 1998

13. P-adic Banach spaces and families of modular forms

    Robert F. Coleman in Inventiones mathematicae

    Article 01 September 1997

14. Classical and overconvergent modular forms

    Robert F. Coleman in Inventiones mathematicae

    Article 01 January 1996

15. Computational problems in arithmetic of linear differential equations. Some diophantine applications

    D. V. Chudnovsky, G. V. Chudnovsky in Number Theory

    Conference paper 1989
    

16. p-adic modular forms

    Fernando Quadros Gouvêa in Arithmetic of p-adic Modular Forms

    Chapter 1988
    

17. The hecke and U operators

    Fernando Quadros Gouvêa in Arithmetic of p-adic Modular Forms

    Chapter 1988
    

18. Galois representations

    Fernando Quadros Gouvêa in Arithmetic of p-adic Modular Forms

    Chapter 1988