Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4665359 | Advances in Mathematics | 2015 | 97 Pages |
Abstract
We show a Riemann–Roch theorem for group ring bundles over an arithmetic surface; this is expressed using the higher adeles of Beilinson–Parshin and the tame symbol via a theory of adelic equivariant Chow groups and Chern classes. The theorem is obtained by combining a group ring coefficient version of the local Riemann–Roch formula as in Kapranov–Vasserot with results on K-groups of group rings and an explicit description of group ring bundles over P1P1. Our set-up provides an extension of several aspects of the classical Fröhlich theory of the Galois module structure of rings of integers of number fields to arithmetic surfaces.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
T. Chinburg, G. Pappas, M.J. Taylor,