Arithmetic surfaces and adelic quotient groups
Abstract
We explicitly calculate an arithmetic adelic quotient group for a locally free sheaf on an arithmetic surface when the fibre over the infinite point of the base is taken into account. The result is stated in the form of a short exact sequence. We relate the last term of this sequence to the projective limit of groups which are finite direct products of copies of the onedimensional real torus and are connected with the first cohomology groups of locally free sheaves on the arithmetic surface.
 Publication:

Izvestiya: Mathematics
 Pub Date:
 August 2018
 DOI:
 10.1070/IM8759
 arXiv:
 arXiv:1801.02282
 Bibcode:
 2018IzMat..82..817O
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Number Theory
 EPrint:
 21 pages