Values at CM points of nearly rigid modular forms
I will explain the main result of C.Franc’s thesis.
Beilinson-Flach classes
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.
A rigid analytic approach to singular moduli (II)
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.
Picard modular surfaces and families of automorphic forms (I)
p-adic families of modular forms as constructed first by Hida and in greater generality by Coleman and their generalizations are a great tool in modern number theory that appears in different parts of the Langlands program.
Picard modular surfaces and families of automorphic forms (II)
p-adic families of modular forms as constructed first by Hida and in greater generality by Coleman and their generalizations are a great tool in modern number theory that appears in different parts of the Langlands program.
Gross-Kudla-Schoen diagonal cycles
Refined conjectures of the Birch and Swinnerton-Dyer type
Based on: B. Mazur, J. Tate, Refined conjectures of the Birch and Swinnerton-Dyer type, Duke Math Journal, vol. 54 1987.
Elliptic units for real quadratic fields
Based on the paper H. Darmon, S. Dasgupta. “Elliptic units for real quadratic fields”.