l-Adic Representations and their Associated Invariants

TL;DR

This paper provides an introductory overview of l-adic Galois representations over local fields, focusing on their representation theory and computational aspects, without delving into varieties or etale cohomology.

Contribution

It offers a simplified, computationally oriented introduction to l-adic Galois representations, emphasizing their structure over local fields.

Findings

Clarifies the theory of l-adic Galois representations

Highlights computational approaches in the study of these representations

Serves as an educational resource for graduate students

Abstract

These are notes from a 3-lecture course given by V. Dokchitser at the ICTP in Trieste, Italy, 1st--5th of September 2014, as part of a graduate summer school on "L-functions and modular forms". The course is meant to serve as an introduction to l-adic Galois representations over local fields with "l not equal to p", and has a slightly computational bent. It is worth mentioning that the course is not about varieties and their etale cohomology, but merely about the representation theory.