Dictionary

algebraic fundamental group en · NOUN

Meanings

1. A group which is an analogue for schemes of the fundamental group for topological spaces.
   • In order to work in arbitrary characteristic, we should use the algebraic fundamental group, which we denote by #92;pi#95;1. (A very good introduction to algebraic fundamental groups is [24].[…]) 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:
   • Neves and Papadakis ([NP09]) constructed a numerical Campedelli surface with algebraic fundamental group #92;mathbbZ#95;6, while Lee and Park ([LP09]) constructed one with algebraic fundamental group #92;mathbbZ#95;2, and one with algebraic fundamental group #92;mathbbZ#95;3 was added in the second version of the same paper. 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:
   • 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, 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).

Forms

Relateds

orbifold fundamental group · fundamental group · geometric fundamental group · topological fundamental group

Synonyms

étale fundamental group (algebraic analogue of fundamental group)