Bounds for Mordell-Weil ranks via Fourier coefficients of automorphic forms on Mp(2)
Let E be an elliptic curve of conductor N defined over the rationals, K a quadratic extension of absolute discriminant D, and e the sign of the Hasse-Weil L-function of E over K.
Lifts of Hilbert modular forms and application to a conjecture of Gross
In this talk, we prove the existence of certain lifts of Hilbert modular forms to general odd spin groups.
Perfectoid spaces I
Perfectoid spaces are specially interesting instances of adic spaces.
A bounded Beilinson-Flach Euler system for a pair of non-ordinary forms
Building on the previous talk, I will set up the construction of a (flat, sharp) integral Euler system associated to the Rankin-Selberg product for a pair of non-ordinary modular forms and also show the Iwasawa theoretic results one can obtain from the same.
p-adic Asai L-functions for Bianchi modular forms
The Asai (or twisted tensor) L-function attached to a Bianchi modular form is the ‘restriction to the rationals’ of the standard L-function. Introduced by Asai in 1977, subsequent study has linked its special values to the arithmetic of the corresponding form.
Espais àdics feixistes
Estudiarem com definir un candidat a feix estructural per a un espai afinoide (de la forma Spa(A,A^+)) i en quins casos surt un feix.
What is…a Darmon point?
The theory of Heegner points, which form a supply of algebraic points on a given elliptic curve, are one of the main tools used in proving the known cases of the Birch and Swinnerton-Dyer conjecture.
Recent topics in elliptic and hyperelliptic curve cryptography
I am going to talk about recent topics in cryptographic theory based on elliptic and hyperelliptic curves. I will start with a general introduction on the elliptic and hyperelliptic curve cryptograpy (ECC) then explain certan recent attacks to ECC and security analysis against these attacks, including results from my own group. In particular, ECC defined…
A rigid analytic approach to singular moduli (I)
The theory of complex multiplication gives a very satisfactory method for constructing abelian extensions of imaginary quadratic fields, by means of the j-invariant attached to certain CM elliptic curves, and some related invariants.
The eigencurve at irregular weight one Eisenstein points
In 1972, Serre observed that the Hecke eigenvalues of Eisenstein series can be p-adically interpolated. In other words, Eisenstein series can be viewed as a p-adic family parametrized by the weight.