Abstract
a class (ON) in the Grothendieck group Ko(Z[G]) of all finitely generated projective Z[G]-modules. The class group Cl(Z[G]) of Z[G] is defined to be the quotient of Ko(Z[G]) by the subgroup generated by the class of Z[G]. Let (ON)stab be the image of (ON) in Cl(Z[G]). In [34] Taylor proved Fr6hlich's conjecture that (ON)stab is equal to another invariant WN/K in Cl(Z[G]) which Cassou-Nogues had defined by means of the root-numbers of symplectic representations of the Galois group G. The root-number of a representation V of G is the constant which appears in the functional equation of the Artin Lfunction of V. The connection between Galois-structure invariants and Artin L-functions has been a basic theme in research on Galois structure; for further discussion, see [12] and [4].
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