Galois Coverings of the Non-Archimedean Projective Line.
Galois Covers and the Hilbert-Grunwald Property
Our main result combines three topics: it contains a Grunwald-Wang type conclusion, a version of Hilbert’s irreducibility theorem and a -adic form à la Harbater, but with good reduction, of the Regular Inverse Galois Problem. As a consequence we obtain a statement that questions the RIGP over . The general strategy is to study and exploit the good reduction of certain twisted models of the covers and of the associated moduli spaces.
Galois covers with prescribed fibers : the Beckmann-Black problem
Galois groups of fields of definition of solvable branched coverings
Galois Properties of Torsion Points on Abelian Varieties.
Galois representations of octahedral type and 2-coverings of elliptic curves.
Galois representations on profinite braid groups on curves.
Galois rigidity of the étale fundamental groups of punctured projective lines.
Galois structure of de Rham cohomology
Galois theory and torsion points on curves
In this paper, we survey some Galois-theoretic techniques for studying torsion points on curves. In particular, we give new proofs of some results of A. Tamagawa and the present authors for studying torsion points on curves with “ordinary good” or “ordinary semistable” reduction at a given prime. We also give new proofs of : (1) the Manin-Mumford conjecture : there are only finitely many torsion points lying on a curve of genus at least embedded in its jacobian by an Albanese map; and (2) the...
Galois theory, elliptic curves, and root numbers
Galois theory of -difference equations
Choose with . The main theme of this paper is the study of linear -difference equations over the field of germs of meromorphic functions at . A systematic treatment of classification and moduli is developed. It turns out that a difference module over induces in a functorial way a vector bundle on the Tate curve that was known for modules with ”integer slopes“, [Saul, 2]). As a corollary one rediscovers Atiyah’s classification of the indecomposable vector bundles on the complex Tate...
Galois theory of special trinomials.
This is the material which I presented at the 60th birthday conference of my good friend José Luis Vicente in Seville in September 2001. It is based on the nine lectures, now called sections, which were given by me at Purdue in Spring 1997. This should provide a good calculational background for the Galois theory of vectorial ( = additive) polynomials and their iterates.
Galoisgruppen über aufgeschlossenen reellen Funktionskörpern.
Gap orders of meromorphic functions on Riemann surfaces.
Gap orders of rational functions on plane curves with few singular points.
Gap Sequences and Moduli in Genus 4.
Gauss sums and algebraic cycles
Gauss Sums and Elliptic Functions. I. The Kummer Sum.
Gaussian maps and multiplication maps on certain projective varieties