Etale Cohomology

Some motivation for p-adic Hodge theory

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 p-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!


Kummer theory and the weak Mordell-Weil theorem

In this post we discuss the notion of Kummer theory in its general form, and how this leads to a proof of the (weak) Mordell-Weil theorem.