Lecture Hall, 6F, Astronomy-Mathematics Building, NTU

(台灣大學天文數學館 六樓演講廳)

p-adic Hodge Theory via the Mysterious Curve

Jean-Marc Fontaine (Université Paris-Sud)

Abstract:

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.

Abstract: events_1_1809044127125164.pdf