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arxiv: 0803.0148 · v3 · pith:CSAGVC4Lnew · submitted 2008-03-03 · 🧮 math.AG · math.NT

Global analytic geometry

classification 🧮 math.AG math.NT
keywords analyticnotiondefinespacevaluationglobalnon-archimedeanring
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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.

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