Section conjecture

In anabelian geometry, a branch of algebraic geometry, the section conjecture gives a conjectural description of the splittings of the group homomorphism

is a complete smooth curve of genus at least 2 over a field

, in terms of decomposition groups of rational points of

The conjecture was introduced by Alexander Grothendieck (1997) in a 1983 letter to Gerd Faltings.

This algebraic geometry–related article is a stub.