Introductory course on $\ell$-adic sheaves and their ramification theory on curves

TL;DR

This paper provides an introductory overview of $\,ell$-adic sheaves and their ramification theory on algebraic curves, based on lectures from a summer school, aiming to educate newcomers in the field.

Contribution

It offers a comprehensive beginner-friendly exposition of $\,ell$-adic sheaves and ramification theory on curves, filling a gap in accessible educational resources.

Findings

Clarifies the fundamental concepts of $\,ell$-adic sheaves.

Explains the ramification theory on algebraic curves.

Provides pedagogical insights from lecture notes.

Abstract

These are the notes accompanying 13 lectures given by the authors at the Clay Mathematics Institute Summer School 2014 in Madrid. The notes give an introduction into the theory of $\ell$-adic sheaves with emphasis on their ramification theory on curves.