01889 - Galois Groups and Fundamental Groups.pdf

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This book explores recent research underlining the remarkable connections
between the algebraic and arithmetic world of Galois theory and the topo-
logical and geometric world of fundamental groups. Arising from an MSRI
program held in the fall of 1999, it contains ten articles, all of which aim to
present new results in a context of expository introductions to theories that
are ramifications and extensions of classical Galois theory.
B. H. Matzat and M. van der Put introduce differential Galois theory and
solve the differential inverse Galois problem over global fields in positive char-
acteristic; D. Harbater gives a comparative exposition of formal and rigid
patching starting from the familiar complex case. S. Mochizuki discusses as-
pects of Grothendieck’s famous anabelian geometry, while the articles by R.
Guralnick, A. Tamagawa, and F. Pop and M. Sa¨ investigate the structure
ıdi
of the fundamental groups of curves over different kinds of characteristic
p
fields. M. Imbert and L. Schneps study the structure of the Hurwitz spaces
and moduli spaces of curves, which are of great importance to Galois theory
because of the Galois action on their fundamental groups. The first interest-
ing such group is SL
2
(Z), a family of special subgroups of which is studied by
F. Bogomolov and Y. Tschinkel. Finally, R. Hain and M. Matsumoto present
their result proving part of a conjecture by Deligne on the structure of the
Lie algebra associated to the Galois action on the fundamental group of the
thrice-punctured projective plane.
Mathematical Sciences Research Institute
Publications
41
Galois Groups and Fundamental Groups
Mathematical Sciences Research Institute Publications
1
2
3
4
5
6
7
8
9
10–11
12–13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
Freed/Uhlenbeck:
Instantons and Four-Manifolds,
second edition
Chern (ed.):
Seminar on Nonlinear Partial Differential Equations
Lepowsky/Mandelstam/Singer (eds.):
Vertex Operators in Mathematics and Physics
Kac (ed.):
Infinite Dimensional Groups with Applications
Blackadar:
K-Theory
for Operator Algebras,
second edition
Moore (ed.):
Group Representations, Ergodic Theory, Operator Algebras, and
Mathematical Physics
Chorin/Majda (eds.):
Wave Motion: Theory, Modelling, and Computation
Gersten (ed.):
Essays in Group Theory
Moore/Schochet:
Global Analysis on Foliated Spaces
Drasin/Earle/Gehring/Kra/Marden (eds.):
Holomorphic Functions and Moduli
Ni/Peletier/Serrin (eds.):
Nonlinear Diffusion Equations and Their Equilibrium States
Goodman/de la Harpe/Jones:
Coxeter Graphs and Towers of Algebras
Hochster/Huneke/Sally (eds.):
Commutative Algebra
Ihara/Ribet/Serre (eds.):
Galois Groups over
Concus/Finn/Hoffman (eds.):
Geometric Analysis and Computer Graphics
Bryant/Chern/Gardner/Goldschmidt/Griffiths:
Exterior Differential Systems
Alperin (ed.):
Arboreal Group Theory
Dazord/Weinstein (eds.):
Symplectic Geometry, Groupoids, and Integrable Systems
Moschovakis (ed.):
Logic from Computer Science
Ratiu (ed.):
The Geometry of Hamiltonian Systems
Baumslag/Miller (eds.):
Algorithms and Classification in Combinatorial Group Theory
Montgomery/Small (eds.):
Noncommutative Rings
Akbulut/King:
Topology of Real Algebraic Sets
Judah/Just/Woodin (eds.):
Set Theory of the Continuum
Carlsson/Cohen/Hsiang/Jones (eds.):
Algebraic Topology and Its Applications
Clemens/Koll´r (eds.):
Current Topics in Complex Algebraic Geometry
a
Nowakowski (ed.):
Games of No Chance
Grove/Petersen (eds.):
Comparison Geometry
Levy (ed.):
Flavors of Geometry
Cecil/Chern (eds.):
Tight and Taut Submanifolds
Axler/McCarthy/Sarason (eds.):
Holomorphic Spaces
Ball/Milman (eds.):
Convex Geometric Analysis
Levy (ed.):
The Eightfold Way
Gavosto/Krantz/McCallum (eds.):
Contemporary Issues in Mathematics Education
Schneider/Siu (eds.):
Several Complex Variables
Billera/Bj¨rner/Green/Simion/Stanley (eds.):
New Perspectives in Geometric
o
Combinatorics
Haskell/Pillay/Steinhorn (eds.):
Model Theory, Algebra, and Geometry
Bleher/Its (eds.):
Random Matrix Models and Their Applications
Schneps (ed.):
Galois Groups and Fundamental Groups
Nowakowski (ed.):
More Games of No Chance
Montgomery/Schneider (eds.):
New Directions in Hopf Algebras
Buhler/Stevenhagen (eds.):
Algorithmic Number Theory
Jensen/Ledet/Yui:
Generic Polynomials: Constructive Aspects of the Inverse Galois
Problem
Q
Volumes 1–4 and 6–27 are published by Springer-Verlag

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