Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Galois modules, ideal class groups and cubic structures   We establish a connection between the theory of cyclotomic ideal class groups
and the theory of "geometric" Galois modules and obtain results on the Galois
module structure of coherent cohomology groups of Galois covers of varieties
over Z. In particular, we show that an invariant that measures the obstruction
to the existence of a virtual normal integral basis for the coherent cohomology
of such covers is annihilated by a product of certain Bernoulli numbers with
orders of even K-groups of Z. We also show that the existence of such a normal
integral basis is closely connected to the truth of the Kummer-Vandiver
conjecture for the prime divisors of the degree of the cover. Our main tool is
a theory of "hypercubic structures" for line bundles over group schemes.

37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio