Editing Algebraic number theory (section)

==Related areas==
Algebraic number theory interacts with many other mathematical disciplines. It uses tools from [[homological algebra]]. Via the analogy of function fields vs. number fields, it relies on techniques and ideas from algebraic geometry. Moreover, the study of higher-dimensional schemes over '''Z''' instead of number rings is referred to as [[arithmetic geometry]]. Algebraic number theory is also used in the study of [[arithmetic hyperbolic 3-manifold]]s.