Section conjecture

In anabelian geometry, a branch of algebraic geometry, the section conjecture gives a conjectural description of the splittings of the group homomorphism formula_1, where formula_2 is a complete smooth curve of genus at least 2 over a field formula_3 that is finitely generated over formula_4, in terms of decomposition groups of rational points of formula_2. The conjecture was introduced by in a 1983 letter to Gerd Faltings.