Relative ampleness in rigid geometry
نویسندگان
چکیده
منابع مشابه
Relative Ampleness in Rigid Geometry
We develop a rigid-analytic theory of relative ampleness for line bundles and record some applications to faithfully flat descent for morphisms and proper geometric objects. The basic definition is fibral, but pointwise arguments from the algebraic and complex-analytic cases do not apply, so we use cohomological properties of formal schemes over completions of local rings on rigid spaces. An an...
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1.1. Motivation. The aim of this paper is to develop a rigid-analytic theory of relative ampleness for line bundles, and to record some applications to rigid-analytic faithfully flat descent for morphisms and for proper geometric objects equipped with a relatively ample line bundle. (For coherent sheaves on rigid spaces, the theory of faithfully flat descent is established in [BG] via Raynaud’s...
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The idea is simple: we want to develop a theory of analytic manifolds and spaces over fields equipped with an arbitrary complete valuation. Of course, it is a standard fact that such a field must be either R, C, or a field with a nonarchimedean valuation, so what we really mean is that we want to develop a theory of nonarchimedean analytic spaces. Doing this näıvely (i.e., defining manifolds in...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2006
ISSN: 0373-0956,1777-5310
DOI: 10.5802/aif.2207