SMS scnews item created by Bill Unger at Wed 19 Feb 2020 1225
Type: Seminar
Distribution: World
Expiry: 21 Feb 2020
Calendar1: 20 Feb 2020 1505-1600
CalLoc1: Carslaw 535A
CalTitle1: Computing Galois groups over p-adic fields

Computational Algebra Seminar: Doris -- Computing Galois groups over p-adic fields

Speaker: Christopher Doris (Bristol)
Title: Computing Galois groups over p-adic fields
Time & Place: 3pm, Thursday 20 February, Carslaw 535

We present a family of algorithms for computing the Galois group of a polynomial
defined over a p-adic field. Apart from the “naive” 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.