Galleries in Poincaré half-spaces and diophantine approximation.
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 algebras and their homomorphisms.
Galois characters associated to formal -modules
Galois co-descent for étale wild kernels and capitulation
Let be a number field with ring of integers . For a fixed prime number and the étale wild kernels are defined as kernels of certain localization maps on the -fold twist of the -adic étale cohomology groups of . These groups are finite and coincide for with the -part of the classical wild kernel . They play a role similar to the -part of the -class group of . For class groups, Galois co-descent in a cyclic extension is described by the ambiguous class formula given by genus theory....
Galois cohomology and Galois representations.
Galois cohomology of biquadratic extensions.
Galois cohomology of special orthogonal groups.
Galois cohomology of the classical gorups over fields of cohomological dimension ... 2.
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 of over with prescribed local or global behavior by specialization
This paper considers some refined versions of the Inverse Galois Problem. We study the local or global behavior of rational specializations of some finite Galois covers of .
Galois descent and cohomology for algebraic groups.
Galois descent and twists of an abelian variety
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 Extensions with Bounded Ramifaction in Characteristic p. On a question of S. Abhyankar.
Galois ...-factors modulo roots of unity.
Galois generators and the subspace theorem.
Galois groups of exponent two and the Brumer-Stark conjecture.
Galois groups of tamely ramified -extensions
Very little is known regarding the Galois group of the maximal -extension unramified outside a finite set of primes of a number field in the case that the primes above are not in . We describe methods to compute this group when it is finite and conjectural properties of it when it is infinite.