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Examples ofresidue field

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The image of a place is a field called theresiduefieldof "p".

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In this article, a local field is non-archimedean and has finiteresiduefield.

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Equivalently, the product is over all points whoseresiduefieldis finite.

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However, some authors consider a more general notion, requiring only that theresiduefieldbe perfect, not necessarily finite.

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There is an equivalent definition of non-archimedean local field: it is a field that is complete with respect to a discrete valuation and whoseresiduefieldis finite.

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From the geometric point of view, "n" -dimensional local fields with last finiteresiduefieldare naturally associated to a complete flag of subschemes of an "n" -dimensional arithmetic scheme.

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Since morphisms of fields are injective, the surjection of the residue fields induced by "g" is an isomorphism.

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Finally, the morphism on residue fields may be assumed to be an isomorphism.

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In contrast to one-dimensional local fields, higher local fields have a sequence of residue fields.

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These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.

单词	residue field
释义	BETA Examples ofresidue field Dictionary> Examples ofresidue field residue fieldisn’t in the Cambridge Dictionary yet. You can help! Add a definition The image of a place is a field called theresiduefieldof "p". From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. In this article, a local field is non-archimedean and has finiteresiduefield. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Equivalently, the product is over all points whoseresiduefieldis finite. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. However, some authors consider a more general notion, requiring only that theresiduefieldbe perfect, not necessarily finite. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. There is an equivalent definition of non-archimedean local field: it is a field that is complete with respect to a discrete valuation and whoseresiduefieldis finite. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. From the geometric point of view, "n" -dimensional local fields with last finiteresiduefieldare naturally associated to a complete flag of subschemes of an "n" -dimensional arithmetic scheme. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Since morphisms of fields are injective, the surjection of the residue fields induced by "g" is an isomorphism. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Finally, the morphism on residue fields may be assumed to be an isomorphism. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. In contrast to one-dimensional local fields, higher local fields have a sequence of residue fields. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
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