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Logic Prizes et Cætera
I discuss the origin and development of logic prizes around the world. In a first section I describe how I started this project by creating the Newton...
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Reconstructing global fields from dynamics in the abelianized Galois group
We study a dynamical system induced by the Artin reciprocity map for a global field. We translate the conjugacy of such dynamical systems into...
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On the Prym map of cyclic coverings
We work out the cases in which the Prym map is dominant and generically finite for étale or totally ramified cyclic coverings.
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On l-adic Galois L-functions
Let \({z}\;\in \;\mathbb{Q}\) and let γ be an l-adic path on...
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Difference between l-adic Galois representations and pro-l outer Galois representations associated to hyperbolic curves
Let l be a prime number, and k a field of characteristic zero. In the present paper, we consider the issue of whether or not the image of the pro- l ...
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Constructing Buildings and Harmonic Maps
In a continuation of our previous work [21], we outline a theory which should lead to the construction of a universal pre-building and versal...
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A remark on the decomposition of the Jacobian variety of Fermat curves of prime degree
Recently, Barraza–Rojas have described the action of the full automorphisms group on the Fermat curve of degree p , for p a prime integer, and...
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Kodaira fibrations and beyond: methods for moduli theory
Kodaira fibred surfaces are remarkable examples of projective classifying spaces, and there are still many intriguing open questions concerning them,...
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The group algebra decomposition of Fermat curves of prime degree
We describe the action of the full automorphisms group on the Fermat curve of degree N . For N prime, we obtain the group algebra decomposition of the...
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The gonality sequence of a curve with an involution
If a curve X of genus g is a double covering of a curve C of genus h such that g ≥ 6 h −3 ≥ 9, there is an explicit relation between the gonality...
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Hyperelliptic curves among cyclic coverings of the projective line, II
In this note, we prove a necessary and sufficient condition for whether a d -cyclic covering of the complex projective line has gonality 2 (i.e., is...
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A local-global principle for torsors under geometric prosolvable fundamental groups
We prove a local-global principle for torsors under the prosolvable geometric fundamental group of a hyperbolic curve over a number field .
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Hyperelliptic curves among cyclic coverings of the projective line, I
In this note, we prove a necessary and sufficient condition for whether a d -cyclic covering of the complex projective line with 3 branch points has...
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On the Fundamental Groups of Non-generic \(\mathbb{R}\) -Join-Type Curves
An \(\mathbb{R}\)...
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Harmonic analysis on the Iwahori–Hecke algebra
These are purely expository notes of Opdam’s analysis [O1] of the trace form τ ( f ) = f ( e ) on the Hecke algebra H = C c ( I \ G / I ) of compactly supported...
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Extension of Galois Groups by Solvable Groups, and Application to Fundamental Groups of Curves
The issue of extending a given Galois group is conveniently expressed in terms of embedding problems. If the kernel is an abelian group, a natural...
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An Octahedral Galois-Reflection Tower of Picard Modular Congruence Subgroups
Between tradition (Hilbert́s 12th Problem) and actual challenges (coding theory) we attack infinite two-dimensional Galois theory. From a number...
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Irreducible Components of Hurwitz Spaces of Coverings with Two Special Fibers
In this paper we prove new results of irreducibility for Hurwitz spaces of coverings whose monodromy group is a Weyl group of type B ...