// Workers AI · dad joke modeWhy was the section conjecture sad? It had a divided opinion.

In anabelian geometry, a branch of algebraic geometry, the section conjecture gives a conjectural description of the splittings of the group homomorphism $\pi _{1}(X)\to \operatorname {Gal} (k)$, where $X$ is a complete smooth curve of genus at least 2 over a field $k$ that is finitely generated over $\mathbb {Q}$, in terms of decomposition groups of rational points of $X$. The conjecture was introduced by Alexander Grothendieck (1997) in a 1983 letter to Gerd Faltings.

References

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

External links

• "Why is the section conjecture important?". mathoverflow.net.