Type: Seminar

Distribution: World

Expiry: 21 Feb 2020

CalTitle1: Computing Galois groups over p-adic fields

Auth: billu@laplace.maths.usyd.edu.au

Speaker: Christopher Doris (Bristol) Title: Computing Galois groups over p-adic fields Time & Place: 3pm, Thursday 20 February, Carslaw 535 Abstract: We present a family of algorithms for computing the Galois group of a polynomial defined over a p-adic field. Apart from the â€œnaiveâ€ algorithm, these are the first general algorithms for this task. This is a version of the well-known resolvent method, initially due to Stauduhar, which is the state-of-the-art for number fields, but a number of features of p-adic fields mean our approach is somewhat different. As an application, we have computed the Galois groups of all totally ramified extensions of Q2 of degrees 18, 20 and 22, tables of which are available online.