algebraic fundamental group

Noun

(algebraic geometry) A group which is an analogue for schemes of the fundamental group for topological spaces.

Japanese Meaning

代数的基本群：代数幾何学の文脈で、スキームに対しトポロジカルな空間における基本群の概念に類似した概念を与える群。 / スキームのエタール被覆を用いることで、従来の基本群の概念を代数的に捉えるための群の構造。

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Google Translation / DeepL Translation

代数幾何学では、スキームに対する代数的基本群が位相空間の基本群に対応する類似物としての役割を果たす。

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Sense（1）

(algebraic geometry) A group which is an analogue for schemes of the fundamental group for topological spaces.

Serre constructed an example of an algebraic variety X over a number field K plus two embeddings of K into ℂ such that the geometric fundamental groups of X_1( ℂ) and X_2( ℂ) are not isomorphic, while the algebraic fundamental groups (i.e. their profinite completions) clearly are isomorphic, see (Serre).

Google Translation / DeepL Translation

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algebraic fundamental groups

（ plural ）

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algebraic fundamental group

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