Galois module structure in weakly ramified 3-extensions
Galois module structure of abelian extensions.
Galois module structure of generalized jacobians.
For a prime number l and for a finite Galois l-extension of function fields L / K over an algebraically closed field of characteristic p <> l, it is obtained the Galois module structure of the generalized Jacobian associated to L, l and the ramified prime divisors. In the cyclic case an implicit integral representation of the Jacobian is obtained and this representation is compared with the explicit representation.
Galois module structure of ideals in wildly ramified cyclic extensions of degree
Galois module structure of ideals in wildly ramified cyclic extensions of degree
For , any totally ramified cyclic extension of degree of local fields which are finite extensions of the field of -adic numbers, we describe the -module structure of each fractional ideal of explicitly in terms of the indecomposable -modules classified by Heller and Reiner. The exponents are determined only by the invariants of ramification.
Galois module structure of integers of relative abelian extensions.
Galois module structure of Kummer orders and elliptic units.
Galois module structure of rings of integers
Let be a Galois extension of number fields with Gal and with property that the divisors of are non-ramified in . We denote the ring of integers of by and we study as a -module. In particular we show that the fourth power of the (locally free) class of is the trivial class. To obtain this result we use Fröhlich’s description of class groups of modules and his representative for the class of , together with new determinantal congruences for cyclic group rings and corresponding congruences...
Galois Module Structure of Rings of Intergers.
Galois module structure of the rings of integers in wildly ramified extensions
The main results of this paper may be loosely stated as follows.Theorem.— Let and be sums of Galois algebras with group over algebraic number fields. Suppose that and have the same dimension and that they are identical at their wildly ramified primes. Then (writing for the maximal order in )In many cases The role played by the root numbers of and at the symplectic characters of in determining the relationship between the -modules and is described. The theorem includes...
Galois module structure of units in real biquadratic number fields
Galois modules and embedding problems.
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 representations
Galois representations, embedding problems and modular forms.
To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations...
Galois representations, Hecke operators, and the cohomology of with twisted coefficients.
Galois representations into GL2(Zp[[X]]) attached to ordinary cusp forms.
Galois representations modulo p and cohomology of Hilbert modular varieties
Galois representations of dihedral type over ℚₚ
Galois representations of Iwasawa modules