## A projective invariant comparing rings of integers in wildly ramified extensions.(English)Zbl 0713.11077

In this paper a “Galois invariant” lying in the class group, $${\mathcal C}\ell ({\mathbb{Z}}\Gamma)$$, is presented. This invariant compares the module structures of the rings of integers of two Galois extensions (with group $$\Gamma$$) which are identical at their wildly ramified primes. The invariant is described in terms of symplectic Gauss sums and is shown to be the difference between the second Chinburg invariants of the extensions. (And this difference is shown to have the expected value.)
Reviewer: S.M.J.Wilson

### MSC:

 11R33 Integral representations related to algebraic numbers; Galois module structure of rings of integers 11L05 Gauss and Kloosterman sums; generalizations 12F10 Separable extensions, Galois theory
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