IISER MOHALI

Abstract: A number field is called monogenic, if its ring of integers can be generated by a single element over the ring of rational integers. To determine these generators of power integral bases we have to solve a Diophantine equation, called index form equation. This is often reduced to some well-known types of Diophantine equations. In the talk we survey methods to solve these types of equations. Moreover, several results are discussed about monogenity of number fields.