p-进Hodge理论和L-不变量

In this paper we introduce the p-adic Hodge theory developped by Fontaine and others, including the comparision theorems in it, and the topics of L-invariants, including a result of the author. The importance of p-adic Hodge theory was first seen by Grothendieck, who propose the so called functorial conjecture. This conjecture was given precisely by Fontaine and Jansen. Later, it was proved by Faltings and Tuiji. L-invariants can be seen as a topics in p-adic Hodge theory. When the base field is Q, it is well understood. In this paper we will introduce five ways defining the L-invariants. When the base field is a totally real field, not all of these five ways can be generalized. It is Teitebaum's definition and Fontaine-Mazur's that can be generalized. The author's result is to compare these two types of L-invariants.