2003/06/20 by G. Pappas, Pappas, G. · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.AG #math.NT
paper · pdf · doi:10.48550/arxiv.math/0306309
69 pages. New introduction, also a substantial improvement of the main result for Galois covers of Albanese type
openalex publication_date 2003/06/20 · arxiv created 2004/04/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish a connection between the theory of cyclotomic ideal class groups and the theory of "geometric" Galois modules and obtain results on the Galois module structure of coherent cohomology groups of Galois covers of varieties over Z. In particular, we show that an invariant that measures the obstruction to the existence of a virtual normal integral basis for the coherent cohomology of such covers 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 normal integral basis is closely connected to the truth of the Kummer-Vandiver conjecture for the prime divisors of the degree of the cover. Our main tool is a theory of "hypercubic structures" for line bundles over group schemes.