Section conjecture
The template {{Wikify}} has been deprecated since 25 August 2012, and is retained only for old revisions. If this page is a current revision, please remove the template.
 | Template:Wikify is deprecated. Please use a more specific cleanup template as listed in the documentation. |
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 (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, MR1483108