Global analytic geometry
Algebraic Geometry
2013-01-09 v3 Number Theory
Abstract
We define a new type of valuation of a ring that combines the notion of Krull valuation with that of multiplicative seminorm. This definition partially restores the broken symmetry between archimedean and non-archimedean valuations. This also allows us to define a notion of global analytic space that reconciles Berkovich's notion of analytic space of a (Banach) ring with Huber's notion of non-archimedean analytic space. After defining natural generalized valuation spectra and computing the spectrum of Z and Z[X], we define analytic spectra and sheaves of analytic functions on them.
Keywords
Cite
@article{arxiv.0803.0148,
title = {Global analytic geometry},
author = {Frederic Paugam},
journal= {arXiv preprint arXiv:0803.0148},
year = {2013}
}
Comments
39 pages; some references to classical scheme theory suppressed; Journal of Number Theory 129 (2009)