Rdcheck - Glossary of scheme theory

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Glossary of scheme theory¶


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A scheme is
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1.  
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The
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A morphism is called
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A morphism
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If
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<dt class="glossary" id="integral">


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Most important properties of schemes are
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The morphism
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The
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An integral scheme is called
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A morphism of schemes is called
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An
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A scheme
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a point
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a
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a
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Geometric points are what in the most classical cases, for example
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This makes the extension from
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Projective morphisms are defined similarly to affine morphisms:
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The
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The
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A separated morphism is a morphism
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is closed. In algebraic geometry, the above formulation is used because a scheme which is a Hausdorff space is necessarily empty or zero-dimensional. The difference between the topological and algebro-geometric context comes from the topological structure of the fiber product (in the category of schemes)
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Main article:
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The higher-dimensional analog of étale morphisms are
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1) for any
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2)
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A
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A morphism has some property universally if all base changes of the morphism have this property. Examples include
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For a point
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Let
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be the ideal generated by the image of
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is a
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