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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 in a 1983 letter to Gerd Faltings.
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