In this post we will describe the Tate conjecture for varieties over finite fields, focusing on its various forms, and talking about some applications.

# Etale Cohomology

# Some examples of Geometric Galois representations

In this post we discuss the Galois representation associated to a projective scheme , where is a number field. We also discuss how this representation can be computed in several simple cases.

# Etale Cohomology: Motivation

In this series of posts, I will be documenting some aspects of étale cohomology, as I, myself, learn it. This will include a mixture of intuition, technical background, and examples. I will start with material that many readers may already be familiar with, through a course in algebraic geometry–topics such as flatness, smoothness, étaleness, etc.

There is no guarantee, and in fact it isn’t likely, that there will be anything here not present at some other place on the internet. There is also a high probability that some of what I say may be incorrect, either technically or intuitively. That said, I hope that some of my scribblings will be of use to some future learner of this brilliant and beautiful subject.

I will be following several sources, but most seriously will be Lei Fu’s *Etale Cohomology*, Milne’s *Etale Cohomology*, and SGA 4.5.