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Introduction to the paper of Y. Ihara on automorphisms of pure sphere braid groups, I

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Danica Kosanovic and Gautier Ponsinet
Don, 2018-09-27 16:30 - 19:00
MPIM Lecture Hall

1) This is a seminar for topology/geometry and Arithmetics (number theory).

2) Aim: One of the aims of the working group is to understand the
theorem that states the existence of an injection from the absolute
Galois group Gal(\bar(Q)/Q) into the profinite version of the
Grothendieck -Teichmuller group.

Organization: The first three sessions of the working group, concern an
introduction to the paper of Y. Ihara « Automorphisms of Pure Sphere
Braid groups and Galois representations » (The Grothendieck Festschrift
vol II). The idea of this seminar is that one topologist and one
arithmetician explains their point of view, on (a part of) this paper.

For this week we will start with basic tools.
The speakers will be Danica Kosanovic (topology) and Gaultier Ponsinet
(number theory).

For the next week Gaultier Ponsinet will give the part 2 of his talk.
(2nd person tbc).

Gaultier will in particular focus on the following points:
«  The goal is to explain (1.4.1), (1.4.2) and (1.4.3) of Ihara's
article. To do so, we will recall the definition and some properties of
the absolute Galois group of a field, of the fundamental group of a
topological space, and finally, of the étale fundamental group of scheme
which links the two previous objects. The book of T. Szamuely « Galois
groups and fundamental groups » and « The algebraic fundamental group »
of F. Oort are good references. »

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