Arithmetic surfaces and adelic quotient groups

D. V. Osipov
2018 Izvestiya: Mathematics  
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 groups which are finite direct products of copies of one-dimensional real torus and are connected with first cohomology groups of locally free sheaves on the arithmetic surface.
doi:10.1070/im8759 fatcat:yw47vphjizettmdx6qcsnlsz7u