In mathematics, the Grothendieck–Teichmüller group GT is a group closely related to (and possibly equal to) the absolute Galois group of the rational numbers. It was introduced by and named after Alexander Grothendieck and Oswald Teichmüller, based on Grothendieck's suggestion in his 1984 essay Esquisse d'un Programme to study the absolute Galois group of the rationals by relating it to its action on the Teichmüller tower of Teichmüller groupoids Tg,n, the fundamental groupoids of moduli stacks of genus g curves with n points removed.
There are several variations of the group: a pro-l version, which is motivic a k-pro-unipotent version, and a profinite version, which is anabelian Hoshi, Minamide, Mochizuki 2022,Collas 2026; These versions were jointly defined by V. Drinfeld and Y.Ihara.
References General references
Translation in Leningrad Math. J. 2 (1991), no. 4, 829–860.
Further reading Relation to algebraic topology via the little disks operads
Relation to combinatorial anabelian geometry
Notes