CAPITAL REGION ALGEBRA/NUMBER THEORY SEMINAR 


Speaker:       Robert G. Underwood, Auburn University Montgomery

Time:          Wednesday, October 3, at 4:30pm, 

Place:         ES 152A, University at Albany, 

Title:         Nontrivial Tame Extensions Over Hopf Orders  


Abstract: 

Let $K$ be an algebraic number field, $l$ be an odd prime, and let $G$ be
an $l$-elementary abelian group.  Let $\Lambda$ denote a Raynaud order in
$K[G]$, with linear dual ${\cal B}$. In this seminar we extend a theorem
of Greither, Replogle, Rubin and Srivastav to give a nontrivial lower
bound on the collection of generalized \lq\lq Galois module classes\rq\rq\
in the locally free classgroup $Cl(\Lambda)$.
These general Galois module classes are the classes of certain tame
$\Lambda$-extensions called semilocal principal homogeneous spaces over
${\cal B}$. For the case $K={\bf Q}(\zeta_m)$, $\zeta_m$ a primitive
$l^m$th root of unity, $m\ge 1$, we use this lower bound to give examples
of $\Lambda$ in $K[G]$ for which there exist semilocal principal
homogeneous spaces over ${\cal B}$ which are not free $\Lambda$-modules.


Refreshments at 4:15pm in ES 152.