Meaning of algebraic fundamental group | Babel Free

Definitions

A group which is an analogue for schemes of the fundamental group for topological spaces.

Examples

“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).”

“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.”

“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].[…])”

CEFR level