Arithmetic surfaces and adelic quotient groups
Algebraic Geometry
2019-01-01 v2 Number Theory
Abstract
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.
Cite
@article{arxiv.1801.02282,
title = {Arithmetic surfaces and adelic quotient groups},
author = {D. V. Osipov},
journal= {arXiv preprint arXiv:1801.02282},
year = {2019}
}
Comments
21 pages; minor changes; to appear in Izvestiya: Mathematics