Anabelian geometry

Anabel's geometry is a mathematical research program by Alexander Grothendieck on the étale fundamental group in algebraic geometry .

More precisely, it is assumed of certain categories of schemes that the functor has an exact left adjoint for them. ${\displaystyle \pi _{1}}$

An example of such a category is that of the module spaces of curves. The conjecture was proven in 1994 for this case by Florian Pop .

literature

• Florian Pop: Glimpses of Grothendiecks anabelian geometry , in Leila Schneps, P. Lochak Geometric Galois actions 1 , London Mathematical Society Lecturenotes Vol. 242, Cambridge University Press 1997, p. 145
• Grothendieck's letter to Faltings on Anabel's geometry from 1983 can be found here: Online

Web links

• Szamuely, talk at MSRI about Anabelian Geometry 1999

Individual evidence

1. ↑ Pop On Grothendieck's conjecture for birational algebraic geometry , Annals of Mathematics, Vol. 139, 1994, pp. 145-182. See T. Szamuely Groupes de Galois de type fini (d´apres Pop) , Seminaire Bourbaki No. 923, 2002/2003 (French), online on the Szamuely website