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Mathematische Annalen

, Volume 341, Issue 1, pp 71–97 | Cite as

Galois module structure of unramified covers

  • Georgios PappasEmail author
Article

Abstract

We use the theory of n-cubic structures to study the Galois module structure of the coherent cohomology groups of unramified Galois covers of varieties over the integers. Assuming that all the Sylow subgroups of the covering group are abelian, we show that the invariant that measures the obstruction to the existence of a “virtual normal integral basis” 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 basis is closely connected to the truth of the Kummer-Vandiver conjecture for the prime divisors of the degree of the cover.

Mathematics Subject Classification (2000)

11R 19A 14F 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA

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