I will introduce the fundamental curve of -adic Hodge theory constructed by Laurent Fargues and myself. I will explain the construction and main properties of this curve, and describe the classification of vector bundles on the curve. As applications, I will show how one can use this curve

 

(a)  to introduce hierarchy of -adic representations of the absolute Galois group of  of a -adic field , and

 

(b)  to prove the main results of the arithmetic part of -adic Hodge theory giving rise to a complete classification of the so called de Rham representations.