Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Brauer-Kuroda formula for higher S-class numbers in dihedral
  extensions of number fields   Let p be an odd prime and let L/k be a Galois extension of number fields
whose Galois group is isomorphic to the dihedral group of order 2p. Let S be a
finite set of primes of L which is stable under the action of Gal(L/k). The
Lichtenbaum conjecture on special values of the Dedekind zeta function at
negative integers, together with Brauer formalism for Artin's L-functions,
gives a (conjectural) formula relating orders of motivic cohomology groups of
rings of S-integers and higher regulators of S-units of the subextensions of
L/k. In analogy with the classical case of special values at 0, we give an
algebraic proof of this formula, i.e. without using the Lichtenbaum conjecture
nor Brauer formalism. Our method also gives an interpretation of the regulator
term as a higher unit index.

22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con