A cohomological relation of unit groups over quadratic extensions of number fields

Derong Qiu

Published 2015-07-09Version 1

Let $ G $ be a group of order $ 2, $ in this paper, we give a simple cohomological relation for finitely generated $ G-$modules, from which we provide new proofs for some known theorems about unit groups over quadratic extensions of number fields, as well as some new applications on Pell equations, units in CM number fields and class number of number fields.