Section conjecture

In anabelian geometry, a branch of algebraic geometry, the section conjecture gives a conjectural description of the splittings of the group homomorphism $\pi_1(X)\to \operatorname{Gal}(k)$ , where $X$ is a complete smooth curve of genus at least 2 over a field $k$ that is finitely generated over $\mathbb{Q}$ , in terms of decomposition groups of rational points of $X$ . The conjecture was introduced by {{harvs|txt|first=Alexander|last=Grothendieck|year=1997|authorlink=Grothendieck}} in a 1983 letter to Gerd Faltings.

References

{{Citation | last1=Grothendieck | first1=Alexander | author1-link=Alexander Grothendieck | editor1-last=Schneps | editor1-first=Leila | editor2-last=Lochak | editor2-first=Pierre | editor1-link=Leila Schneps|title=Geometric Galois actions, 1 | publisher=Cambridge University Press | series=London Math. Soc. Lecture Note Ser. | isbn= 978-0-521-59642-8 |mr=1483108 | year=1997 | volume=242 | chapter=Brief an G. Faltings | pages=49–58}}

External links

{{cite web|url=https://mathoverflow.net/q/179664 |title=Why is the section conjecture important?|website=mathoverflow.net}}

Category:Algebraic geometry

Category:Unsolved problems in geometry

Category:Arithmetic geometry