Arithmetic surfaces and adelic quotient groups

摘要

We explicitly calculate an arithmetic adelic quotient group for a locallyfree sheaf on an arithmetic surface when the fiber over the infinite point ofthe base is taken into account. The calculations are presented via a shortexact sequence. We relate the last term of this short exact sequence with theprojective limit of free finitely generated modules over the one-dimensionalreal torus such that these modules are connected with first cohomology groupsof locally free sheaves on the arithmetic surface.