Colloquium August 25
Date: Friday August 25
Time: 16:00 to 17:00
Place: 455 McBryde (Commons Room)
Speaker: Nigel Byott of Univ Exeter, England
Title: Realizable Galois module classes for some nonabelian extensions
Abstract
Let k be a number field and
Γ a finite group. We consider
the ring of algebraic integers ON in a Galois extension N of k
with
Gal(N/k)≌Γ as a module for the group ring
OkΓ. If N/k is at most tamely ramified, then ON is a
locally free
OkΓ-module, and determines a class in the
locally free class group
Cl(OkΓ). By extension of scalars, it
therefore determines a class in
Cl(M), where
M
is a maximal
order in
kΓ. I will describe joint work with C. Greither and
B. Sodaïgui, in which we determine the subset
R(M) of classes
in
Cl(M) realized in this way, in the case that
Γ belongs
to a family of nonabelian groups of order
2r(2r - 1) for
r≥2. The argument uses some ideas from coding theory.
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