Article ID Journal Published Year Pages File Type
4665359 Advances in Mathematics 2015 97 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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