An invitation to p-adic Hodge theory, or: How i learned to stop worrying and love period rings

This is the rough outline of a talk I recently gave at the Berkeley Student Algebraic Geometry Seminar on the progression of ideas that might lead one to define the Hodge-Tate decomposition.

Hodge Symmetry in characteristic Zero

In this post we prove that varieties over characteristic fields are all ‘Hodge symmetric’, meaning that .