Exact algorithms for p-adic fields and epsilon constant conjectures

Abstract

We describe an algorithmic approach to prove or disprove several recent conjectures for epsilon constants of Galois extensions of p-adic fields and number fields. For this approach, we must develop various algorithms for computations in Galois extensions of p-adic fields which are of independent interest. Our algorithms for p-adic fields are based on existing algorithms for number fields and are exact in the sense that we do not need to consider approximations to p-adic numbers.