Compactifying Spec Z
Algebraic Geometry
2012-03-26 v2 Number Theory
Abstract
In this paper, we introduce a new algebraic type of `convexoid rings', and we give the definition of (weak) convexoid schemes, which share similar properties with ordinary schemes. As a result, we give a purely-algebraic construction of the compactification of Spec Z (in Arakelov's sense) which is realized as the Zariski-Riemann space in the category of weak convexoid schemes.
Cite
@article{arxiv.1203.4914,
title = {Compactifying Spec Z},
author = {Satoshi Takagi},
journal= {arXiv preprint arXiv:1203.4914},
year = {2012}
}
Comments
29 pages, 1 figure