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Arithmetic surface

In mathematics, an arithmetic surface over a Dedekind domain R {\displaystyle R} with fraction field K {\displaystyle K} is a geometric object having one conventional dimension, and one other dimension provided by the infinitude of the primes. When R {\displaystyle R} is the ring of integers Z {\displaystyle \mathbb {Z} } , this intuition depends on the…

Overview, Over a Dedekind scheme & Examples

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Overview

Formal definition

Over a Dedekind scheme

Properties

Examples

Intersection theory

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Map overview Semantic statistics

Arithmetic surface

Nodes45
Edges44
Triples27
Avg. degree1.96
Density0.044444
Components1

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Arithmetic surface

Top relations

related to Divisors · 5
Arithmetic surface → Hartshorne's Algebraic Geometry, The, This, We, Weil
related to Formal definition · 5
Arithmetic surface → An, Dedekind, Frac, R/t, Spec
related to Intersection theory · 5
Arithmetic surface → Arakelov, Given, In, The, This
related to Over a Dedekind scheme · 4
Arithmetic surface → An, Dedekind, In, This
related to Over Dedekind rings · 3
Arithmetic surface → Arithmetic, Dedekind, In
related to Projective line · 2
Arithmetic surface → Dedekind, The
related to Regular minimal models · 2
Arithmetic surface → Néron, There
related to Dimension · 1
Arithmetic surface → Arithmetic

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Important terminology

arithmetic displaystyle surfaces dimension dedekind surface fiber field intersection theory projective one ring algebraic curves divisors line scheme regular defined

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Arithmetic surfacerelated to DimensionArithmetic0.60section
Arithmetic surfacerelated to DivisorsWe0.60section
Arithmetic surfacerelated to DivisorsWeil0.60section
Arithmetic surfacerelated to DivisorsThis0.60section
Arithmetic surfacerelated to DivisorsThe0.60section
Arithmetic surfacerelated to DivisorsHartshorne's Algebraic Geometry0.60section
Arithmetic surfacerelated to Formal definitionAn0.60section
Arithmetic surfacerelated to Formal definitionDedekind0.60section
Arithmetic surfacerelated to Formal definitionSpec0.60section
Arithmetic surfacerelated to Formal definitionFrac0.60section
Arithmetic surfacerelated to Formal definitionR/t0.60section
Arithmetic surfacerelated to Intersection theoryGiven0.60section

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