In this chapter we will study extra structure in the case when
is Galois over
. We will learn about Frobenius elements,
the Artin symbol, decomposition groups, and how the Galois group of
is related to Galois groups of residue class fields. These are
the basic structures needed to attach -function to representations of
, which will play a central role in the next few
chapters.

**Subsections**

William Stein
2012-09-24