Unit Groups and 2-Class Field Towers; Techniques and Computations

Abstract: During this talk we are going to expose some techniques for computing the unit groups of multiquadratic number fields. Furthermore, we shall present a new simple method to deal with the $2$-class field towers of some number fields whose $2$-class groups are of type $(2,2)$. More precisely, we shall compute the unit group of the number field $\mathbb{Q}( \sqrt{p}, \sqrt{q},\sqrt{2} ,\sqrt{-1})$, where $p$ and $q$ are two prime numbers. In the second part this talk, we shall use units to study the $2$-class field tower of some imaginary biquadratic number fields.

number theory

Audience: researchers in the topic

Algebra and Number Theory Seminars at Université Laval