Lecture----数学院晨兴数学中心

Title:	Point-theoreticity implies geometricity in anabelian geometry
Speaker:	Fucheng Tan (Shanghai Center for Mathematical Sciences and Shanghai Jiao Tong University)
Time:	2015-11-16, 13：30-14：30
Place:	N913
Abstract:	In this talk, I will explain a fundamental result of Shinichi Mochizuki on the absolute pro-Σ anabelian geometry of hyperbolic curves over mixed-characteristic local fields, for Σ a set of primes of cardinality at least 2 that contains the residue characteristic of the base field. In this situation, the condition on an isomorphism of arithmetic fundamental groups of preservation of decomposition groups of closed points implies that the isomorphism arises from an isomorphism of schemes, that is, “point-theoreticity implies geometricity”, a partial "Section Conjecture". Using Mochizuki's earlier work on Grothendieck's anabelian conjecture, one can verify that such a condition on preservation of decomposition groups holds for hyperbolic curves of strictly Belyi type, which are by definition those hyperbolic curves defined over number fields and isogenous to a hyperbolic curve of genus 0.
Attachment: