-тождества и -многообразия
-тождества нильпотентных групп. I
-тождества нильпотентных групп. II
Gale duality for complete intersections
We show that every complete intersection defined by Laurent polynomials in an algebraic torus is isomorphic to a complete intersection defined by master functions in the complement of a hyperplane arrangement, and vice versa. We call systems defining such isomorphic schemes Gale dual systems because the exponents of the monomials in the polynomials annihilate the weights of the master functions. We use Gale duality to give a Kouchnirenko theorem for the number of solutions to a system of master...
Galois actions on Néron models of Jacobians
Let be a smooth curve defined over the fraction field of a complete discrete valuation ring . We study a natural filtration of the special fiber of the Néron model of the Jacobian of by closed, unipotent subgroup schemes. We show that the jumps in this filtration only depend on the fiber type of the special fiber of the minimal regular model with strict normal crossings for over , and in particular are independent of the residue characteristic. Furthermore, we obtain information about...
Galois characters associated to formal -modules
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 between surfaces
We give a classification of finite group actions on a surface giving rise to quotients, from the point of view of their fixed points. It is shown that except two cases, each such group gives rise to a unique type of fixed point set.
Galois covers with prescribed fibers : the Beckmann-Black problem
Galois descent and cohomology for algebraic groups.
Galois descent and twists of an abelian variety
Galois embedding of algebraic variety and its application to abelian surface
Galois extensions of height-one commuting dynamical systems
We consider a dynamical system consisting of a pair of commuting power series under composition, one noninvertible and another nontorsion invertible, of height one with coefficients in the -adic integers. Assuming that each point of the dynamical system generates a Galois extension over the base field, we show that these extensions are in fact abelian, and, using results from the theory of the field of norms, we also show that the dynamical system must include a torsion series. From an earlier...
Galois groups of fields of definition of solvable branched coverings
Galois orbits and equidistribution: Manin-Mumford and André-Oort.
We overview a unified approach to the André-Oort and Manin-Mumford conjectures based on a combination of Galois-theoretic and ergodic techniques. This paper is based on recent work of Klingler, Ullmo and Yafaev on the André-Oort conjecture, and of Ratazzi and Ullmo on the Manin-Mumford conjecture.
Galois Properties of Torsion Points on Abelian Varieties.
Galois representations modulo p and cohomology of Hilbert modular varieties
Galois representations of octahedral type and 2-coverings of elliptic curves.
Galois representations on profinite braid groups on curves.