English

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.

Keywords

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

R2 v1 2026-06-21T20:38:12.180Z