Erratum à l'article «Analogues supérieurs du noyau sauvage»
Étale Galois covers of affine smooth cuves. The geometric case of a conjecture of Shafarevich. On Abhyankar's conjecture.
Euler system for Galois deformations
In this paper, we develop the Euler system theory for Galois deformations. By applying this theory to the Beilinson-Kato Euler system for Hida’s nearly ordinary modular deformations, we prove one of the inequalities predicted by the two-variable Iwasawa main conjecture. Our method of the proof of the Euler system theory is based on non-arithmetic specializations. This gives a new simplified proof of the inequality between the characteristic ideal of the Selmer group of a Galois deformation and the...
Extensions non abéliennes de degré d’un corps de nombres : étude locale-globale
Fields of Cohomological 2-Dimension Three.
Formulations algébriques de la conjecture de Leopoldt et applications
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 of biquadratic extensions.
Galois descent and cohomology for algebraic groups.
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.
Galois modules and embedding problems.
Galoismoduln mit Hasse-Prinzip.
Global restrictions on ramification in number fields.
Infinite class field towers of quadratic fields.
Infinitely ramified Galois representations.
Invariants of a quadratic form attached to a tame covering of schemes
We build on preceeding work of Serre, Esnault-Kahn-Viehweg and Kahn to establish a relation between invariants, in modulo 2 étale cohomology, attached to a tamely ramified covering of schemes with odd ramification indices. The first type of invariant is constructed using a natural quadratic form obtained from the covering. In the case of an extension of Dedekind domains, mains, this form is the square root of the inverse different equipped with the trace form. In the case of a covering of Riemann...
Invariants of number fields related to central embedding problems.
K2-analogs of Hasse's norm theorems.
Kapitulation der Idealklassen und Einheitenstruktur in Zahlkörpern.
Kapitulationsproblem und Knotentheorie.