Arithmetic Cohomology Groups
Algebraic Geometry
2015-07-23 v1
Abstract
We first introduce global arithmetic cohomology groups for quasi-coherent sheaves on arithmetic varieties, adopting an adelic approach. Then, we establish fundamental properties, such as topological duality and inductive long exact sequences, for these cohomology groups on arithmetic surfaces. Finally, we expose basic structures for ind-pro topologies on adelic spaces of arithmetic surfaces. In particular, we show that these adelic spaces are topologically self-dual.
Cite
@article{arxiv.1507.06074,
title = {Arithmetic Cohomology Groups},
author = {K. Sugahara and L. Weng},
journal= {arXiv preprint arXiv:1507.06074},
year = {2015}
}
Comments
42 pages