https://en.wikipedia.org/wiki/P-adic_Hodge_theory p-adic Hodge theory
In mathematics, p-adic Hodge theory is a theory that provides a way to classify and study p-adic Galois representations of characteristic 0 local fields[1] with residual characteristic p (such as Qp). The theory has its beginnings in Jean-Pierre Serre and John Tate's study of Tate modules of abelian varieties and the notion of Hodge?Tate representation. Hodge?Tate representations are related to certain decompositions of p-adic cohomology theories analogous to the Hodge decomposition, hence the name p-adic Hodge theory. Further developments were inspired by properties of p-adic Galois representations arising from the etale cohomology of varieties. Jean-Marc Fontaine introduced many of the basic concepts of the field.
Contents 1 General classification of p-adic representations 2 Period rings and comparison isomorphisms in arithmetic geometry 3 Notes 4 References 4.1 Primary sources 4.2 Secondary sources
