Dokchitser’s Notes on l-adic Representations

It’s always a treat when a set of lecture notes for a workshop find their way to my arXiv RSS feeds. Today I found notes written by Samuele Anni on Vladimir Dokchitser’s lectures $l$-adic representations and their associated invariants (20pp). Here is the 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.

Here is a quotation from the introduction containing the prerequisites:

The prerequisites for the course are fairly modest: the theory of local fields and representation theory of finite groups, such as might be covered in a Masters level course, and, for the sake of examples and motivation, the theory of elliptic curves over local fields (Silverman’s book is more than sufficient). Some previous exposure to L-functions is desirable, as, after all, this was the main topic of the school.

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