Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Galois module structure of the square root of the inverse different over
  maximal orders   Let $K$ be a number field with ring of integers $\mathcal{O}_K$ and let $G$
be a \mbox{finite group of} odd order. Given a $G$-Galois $K$-algebra $K_h$,
let $A_h$ be the square root of the inverse different of $K_h/K$, which exists
by Hilbert's formula. If $K_h/K$ is weakly ramified, then $A_h$ is locally free
over $\mathcal{O}_{K}G$ by a result of B. Erez, in which case it determines a
class in the locally free class group $\mbox{Cl}(\mathcal{O}_KG)$ of
$\mathcal{O}_KG$. Such a class in $\mbox{Cl}(\mathcal{O}_KG)$ is said to be
$A$-realizable, and tame $A$-realizable if $K_h/K$ is tame. Let
$\mathcal{A}(\mathcal{O}_KG)$ and $\mathcal{A}^t(\mathcal{O}_KG)$ denote the
sets of all $A$-realizable classes and tame $A$-realizable classes,
respectively. For $G$ abelian, we will show that the two sets
$\mathcal{A}(\mathcal{O}_KG)$ and $\mathcal{A}^t(\mathcal{O}_KG)$ are equal
when extended scalars to the maximal order in $KG$.

23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con