Posted by Jason Polak on 17. September 2015 · Write a comment · Categories: algebraic-geometry · Tags: , ,

One policy of Aleph Zero Categorical is that any lecture notes posted on the arXiv that I manage to see will be announced and advertised here. Today I saw that Lars Kindler and Kay Rülling have posted their notes entited:

I quote from the introduction for a summary of these notes:

These are the notes accompanying 13 lectures given by the authors at the
Clay Mathematics Institute Summer School 2014 in Madrid. The goal of
this lecture series is to introduce the audience to the theory of $\ell$-adic sheaves
with emphasis on their ramification theory. Ideally, the lectures and these
notes will equip the audience with the necessary background knowledge to
read current literature on the subject, particularly [16], which is the focus of
a second series of lectures at the same summer school. We do not attempt
to give a panoramic exposition of recent research in the subject.

Here, reference 16 refers to the paper “A finiteness theorem for Galois representations of function fields over finite fields (after Deligne)” by Esnault and Kerz. Here is one last quotation that gives the prerequisites for these notes:

The text can roughly be divided into two parts: Sections 2 to 4 deal
with the local theory and only assume a basic knowledge of commutative
algebra, while the following sections are more global in nature and require
some familiarity with algebraic geometry.

The algebraic geometry in these notes is actually quite gentle: they define etale morphism and state basic properties, and the define the etale fundamental group and even prove things about it. Not only that, but these notes have an index!