Section conjecture

In anabelian 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.

References

• Grothendieck, Alexander (1997), "Brief an G. Faltings", in Schneps, Leila; Lochak, Pierre, Geometric Galois actions, 1, London Math. Soc. Lecture Note Ser. 242, Cambridge University Press, pp. 49–58, ISBN 978-0-521-59642-8, MR 1483108