University of Sydney
School of Mathematics and Statistics
University of Heidelberg
On computing automorphisms and subfields.
Friday 26th March, 12-1pm, Carslaw 375.
In this talk we present algorithms for computing automorphisms
and subfields of an algebraic number field K. The computations are
done in unramified p-adic extensions without knowing the Galois
group of (the splitting field of) K. For the subfield computation we
use the fact that the lattice of block systems of the Galois group
of K is isomorphic to the lattice of subfields. We present an algorithm
for computing Frobenius automorphisms of normal number fields.
Using these algorithms we describe an explicit method to compute
automorphisms and subfields of algebraic function fields. In the
number field case it is possible to compute automorphisms and subfields
of fields up to degree 60. In the abelian case it is possible to
compute automorphisms for fields up to degree 200.