ABSTRACT
Throughout this chapter, K denotes an algebraic number field.
1. 1. The torus T
from K to Q , cf. Weil [43], §1. 3. If A is a commutative Qalgebra, the points of T with values in A form by definition the
that E is an algebraic subgroup of T. Let T E be the quotient
a. Let K be quadratic over Q, so that dim T = 2. Let E be the group of units of K. Show that T E is of dimension 2 (resp. 1) if K is imaginary (resp. real).
