Arithmetic surfaces and adelic quotient groups

D. V. Osipov

Published 2018-01-08Version 1

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