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 
These are even less edited than usual, so I profusely apologize for any mistakes. As always, corrections/comments are very welcome!
In this post we compute the Galois representation 
This is the transcription to blog format of a talk I gave at the UC Berkeley Student Arithmetic Geometry Seminar about several topics related to Fontaine’s famous result that there are no abelian schemes over 
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.
In this post we compute the group 
In this post we compute the compactly supported cohomology of some simple varieties.
In this post we will describe the Tate conjecture for varieties over finite fields, focusing on its various forms, and talking about some applications.
