## STNB2017(31è any)

### The eigencurve: geometric construction.

#### Ponents

The aim of this talk is to give a gentle but fairly complete introduction to the Coleman-Mazur eigencurve. I will begin by recall the construction of V.Pilloni of the overconvergent modular sheave using coherent cohomology. After I will give a short introduction about the p-adic spectral theory of the Atkin operator $U_p$ and how we get the Coleman-Mazur eigencurve. I will finish this talk by giving some geometric properties of the Coleman-Mazur Eigencurve. References: [CM96], [Pil13]