The section conjecture, in anabelian geometry, gives a conjectural description of the splittings of the fundamental group homomorphism from a complete smooth curve of genus at least two, defined over a number field, to the Galois group of that field, in terms of the decomposition groups of the curve's rational points. It was introduced by Alexander Grothendieck in a 1983 letter to Gerd Faltings.
Facts
StatementFor a complete smooth curve X of genus at least 2 over a finitely generated field k, describes the splittings of the homomorphism from the fundamental group of X to the Galois group of k in terms of decomposition groups of rational points of X. 1 Proposed Year Classification
Resolution Status Prize Status
Prize Status (category) Connections
In Branch
Source Section Conjecture (Wikipedia)
Posed By
Sources
1. Section Conjecture (Wikipedia)
Lead section
The conjecture was introduced by Alexander Grothendieck (1997) in a 1983 letter to Gerd Faltings.
Lead section [statement]
the section conjecture gives a conjectural description of the splittings of the group homomorphism
In Branch: Algebraic Geometry, Lead sentence
In anabelian geometry, a branch of algebraic geometry, the section conjecture gives a conjectural description of the splittings of
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.