nLab
arithmetic geometry

Contents

Idea

Arithmetic geometry is a branch of algebraic geometry studying schemes (usually of finite type) over the spectrum SpecSpec \mathbb{Z} of the ring of integers, for number theoretic purposes; usually one complements this with some data “at the prime at infinity” leading to a more modern notion of an arithmetic scheme (cf. Arakelov geometry).

References

Revised on November 6, 2013 23:55:02 by Urs Schreiber (82.169.114.243)