"algebraic fundamental group" meaning in All languages combined

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        {
          "text": "1997, Frans Oort, The Algebraic Fundamental Group, Leila Schneps, Pierre Lochak (editors), Geometric Galois Actions 1: Around Grothendieck's Esquisse D'un Programme, Cambridge University Press, London Mathematical Society, page 78,\nSerre 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)."
        },
        {
          "ref": "2011, Ingrid Bauer, Fabrizio Catanese, Roberto Pignatelli, “Surfaces of general type with geometric genus zero: a survey”, in Wolfgang Ebeling, Klaus Hulek, Knut Smoczyk, editors, Complex and Differential Geometry, Springer, page 11",
          "text": "Neves and Papadakis ([NP09]) constructed a numerical Campedelli surface with algebraic fundamental group #x5C;mathbbZ#x5F;6, while Lee and Park ([LP09]) constructed one with algebraic fundamental group #x5C;mathbbZ#x5F;2, and one with algebraic fundamental group #x5C;mathbbZ#x5F;3 was added in the second version of the same paper.",
          "type": "quotation"
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          "ref": "2013, János Kollár, “Rationally Connected Varieties and Connected Groups”, in Károly Böröczky, Jr., János Kollár, Szamuely Tamas, editors, Higher Dimensional Varieties and Rational Points, Springer, page 70",
          "text": "In order to work in arbitrary characteristic, we should use the algebraic fundamental group, which we denote by #x5C;pi#x5F;1. (A very good introduction to algebraic fundamental groups is [24].[…])",
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        "A group which is an analogue for schemes of the fundamental group for topological spaces."
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        "(algebraic geometry) A group which is an analogue for schemes of the fundamental group for topological spaces."
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          "sense": "algebraic analogue of fundamental group",
          "word": "étale fundamental group"
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          "text": "1997, Frans Oort, The Algebraic Fundamental Group, Leila Schneps, Pierre Lochak (editors), Geometric Galois Actions 1: Around Grothendieck's Esquisse D'un Programme, Cambridge University Press, London Mathematical Society, page 78,\nSerre 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)."
        },
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          "ref": "2011, Ingrid Bauer, Fabrizio Catanese, Roberto Pignatelli, “Surfaces of general type with geometric genus zero: a survey”, in Wolfgang Ebeling, Klaus Hulek, Knut Smoczyk, editors, Complex and Differential Geometry, Springer, page 11",
          "text": "Neves and Papadakis ([NP09]) constructed a numerical Campedelli surface with algebraic fundamental group #x5C;mathbbZ#x5F;6, while Lee and Park ([LP09]) constructed one with algebraic fundamental group #x5C;mathbbZ#x5F;2, and one with algebraic fundamental group #x5C;mathbbZ#x5F;3 was added in the second version of the same paper.",
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          "text": "In order to work in arbitrary characteristic, we should use the algebraic fundamental group, which we denote by #x5C;pi#x5F;1. (A very good introduction to algebraic fundamental groups is [24].[…])",
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