section, conjecture, anabelian, geometry, branch, algebraic, geometry, section, conjecture, gives, conjectural, description, splittings, group, homomorphism, displaystyle, operatorname, where, displaystyle, complete, smooth, curve, genus, least, over, field, d. In anabelian geometry a branch of algebraic geometry the section conjecture gives a conjectural description of the splittings of the group homomorphism p 1 X Gal k displaystyle pi 1 X to operatorname Gal k where X displaystyle X is a complete smooth curve of genus at least 2 over a field k displaystyle k that is finitely generated over Q displaystyle mathbb Q in terms of decomposition groups of rational points of X displaystyle X The conjecture was introduced by Alexander Grothendieck 1997 in a 1983 letter to Gerd Faltings References editGrothendieck 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 1483108External links edit Why is the section conjecture important mathoverflow net nbsp This algebraic geometry related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Section conjecture amp oldid 1161308079, wikipedia, wiki, book, books, library,