I will try to upgrade the URL I use below for the various papers into a
web site on "Profinite Arithmetic Geometry, Modular Towers and related
moduli spaces like Shimura varieties." I look for evidence that
featuring the connection between Modular Towers/Regular Inverse Galois
Problem and the Strong Torsion Conjecture will have a serious effect.
Here are things that can go into such a web site:
1. Basic definitions with examples: Universal p-Frattini cover, Modular
Towers, Harbater patching, tangential base points and associated GQ action along towers
of moduli spaces, cusp types, ...
2. Conjectures and connections between them: Dèbes'
generalization of R(egular)I(nverse)G(alois)P(roblem) and
Beckman-Black, Fried-Voelklein (projective + Hilbertian implies
pro-free), Strong Torsion and Main Modular Tower Conjecture, ...
3. Catalog of progress on defining and achieving #1 and #2, include an
archive (through URLs?) of the relevant papers.
If I make it modular enough -- you put the pieces of the site in
through a standard interface -- then maybe it will be easy to run, and
others will contribute.
List of
papers relevant to recent progress on the Main Conjecture on Modular
Towers
Pierre Definitions:
- RIGP
- field of moduli vs field of definition
- branch cycle argument
- Hurwitz spaces and modular towers
- class field theory for function fields
- Harbater's patching
[STMT] A. Cadoret, Modular Towers and Torsion
on Abelian Varieties, preprint as of May, 2006.
[DE] P. D`ebes and M. Emsalem, Harbater-mumford
components and hurwitz towers, Inst. M. Jussieu (200).
[AGLI] M.D. Fried, Alternating groups and
lifting invariants, Out for refereeing (2006), 1--36.
[LUM] M.D. Fried, The Main
Conjecture of Modular Towers and its higher
rank generalization, in Groupes de Galois arithmetiques et
differentiels (Luminy 2004; eds. D. Bertrand and P. D`ebes), Seminaires
et Congres, 13, 2006.
[EXP] M.D. Fried, Regular
realizations of p-projective quotients and modular curve-like towers,
Exposition on the Inverse Galois Problem from a MT viewpoint.
[MCMT] M.D. Fried and D. Semmen, Modular
curve-like Towers and the Inverse Galois Problem, in preparation.
[We] T. Weigel, Maximal p-frattini quotients of p-Poincaré duality
groups of dimension 2, volume for O.H. Kegel on his 70th birthday,
Arkiv der Mathematik--Basel, 2005.