In anabelian geometry, a branch of algebraic geometry, the section conjecture gives a conjectural description of the splittings of the group homomorphism , where is a complete smooth curve of genus at least 2 over a field that is finitely generated over , in terms of decomposition groups of rational points of . The conjecture was introduced by Alexander Grothendieck (1997) in a 1983 letter to Gerd Faltings.
- Grothendieck, Alexander (1997), "Brief an G. Faltings", in Schneps, Leila; Lochak, Pierre (eds.), 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
- "Why is the section conjecture important?". mathoverflow.net.
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