Somnis de joventut p-àdics
Aquesta és la primera d’una sèrie de xerrades per explicar els resultats recents de Darmon i Vonk de construcció (conjectural) d’extensions abelianes de cossos totalment reals avaluant cocicles meromòrfics rígid-analítics p-àdics en punts totalment reals.
The Rank of Mazur’s Eisenstein ideal
In his landmark 1976 paper “Modular curves and the Eisenstein ideal”, Mazur studied congruences modulo p between cusp forms and an Eisenstein series of weight 2 and prime level N.
Topology of spaces of valuations and geometry of singularities I
Given an algebraic variety X defined over a field k, the space of all valuations of the field of rational functions of X extending the trivial valuation on k is a projective limit of algebraic varieties.
Topology of spaces of valuations and geometry of singularities II
Topology of spaces of valuations and geometry of singularities III
Advanced Course: p-adic Cohomologies and Reciprocity Laws
In the first part of this course, we give an overview of the computation of the p-adic cohomology of varieties over local fields using the theory of (phi,Gamma)-modules, following Colmez and Niziol. In the second part, we discuss applications of this theory to the problem of explicit reciprocity laws.
Advanced Course: p-adic Cohomologies and Reciprocity Laws
Some new Hecke modules for arithmetic groups coming from C*-algebras
Given an arithmetic group G, there are two classical Hecke modules associated to G that are of central importance to number theory. Namely, the space of cusp forms associated to G (with fixed weight) and the cohomology of the arithmetic manifold M associated to G (with coefficients in a fixed local system). The Eichler-Shimura isomorphism…