These are some notes that I wrote for a learning course at Berkeley–the goal being to understand the statement of the global Langlands conjecture.
The goal of the talk (that these notes were written for) was, specifically, to motivate -adic Hodge theory with an eye, in particular, towards where it might be useful in understanding the statement of Langlands.
These are even less edited than usual, so I profusely apologize for any mistakes. As always, corrections/comments are very welcome!