Section conjecture

In anabelian geometry, a branch of algebraic geometry, the section conjecture gives a conjectural description of the splittings of π₁(X) → Gal(k), where X is a complete smooth curve of genus at least 2 over a field k that is finitely generated over Q, in terms of decomposition groups of rational points of X. The conjecture was introduced by Grothendieck (1997) in a 1983 letter to Faltings.