Some implications between Grothendieck's anabelian conjectures

Dr. Giulio Bresciani

In his famous letter to Faltings, Grothendieck explained a series of ideas and

conjectures collected under the name of anabelian geometry. Grothendieck's

picture describes how for certain varieties, called anabelian, defined over

fields finitely generated over Q the étale fundamental group recovers all the

geometric information about the variety. In dimension one anabelian varieties

are curves with negative Euler characteristic, but in higher dimension the

picture is not so clear. Some of the anabelian conjectures have been proved,

most notably by Mochizuki. Among the anabelian conjectures, the so called

section conjecture remains largely open. We show how the section conjecture

implies a much stronger anabelian statement, from which every other anabelian

statement follows immediately. We do this in the generality of Deligne-Mumford

stacks, rather than varieties, and show that if the section conjecture holds for

curves then it holds for some other classes of DM stacks.

Nov 22, 2018 | 02:00 PM c.t. - 04:00 PM

A6/SR 007/008