Galois module structure of unramified covers | Zendy

G. Pappas | Zendy

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Galois module structure of unramified covers

Author(s) -

G. Pappas

Publication year - 2007

Publication title -

mathematische annalen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.235

H-Index - 75

eISSN - 1432-1807

pISSN - 0025-5831

DOI - 10.1007/s00208-007-0183-2

Subject(s) - mathematics , galois group , sylow theorems , galois cohomology , pure mathematics , abelian group , fundamental theorem of galois theory , embedding problem , galois module , galois extension , conjecture , cover (algebra) , discrete mathematics , group (periodic table) , finite group , chemistry , organic chemistry , mechanical engineering , engineering

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.

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