A comparison of Selmer groups.
A Grunwald-Wang type theorem for abelian varieties
A Hasse principle for two dimensional global fields.
A note on free pro--extensions of algebraic number fields
For an algebraic number field and a prime , define the number to be the maximal number such that there exists a Galois extension of whose Galois group is a free pro--group of rank . The Leopoldt conjecture implies , ( denotes the number of complex places of ). Some examples of and with have been known so far. In this note, the invariant is studied, and among other things some examples with are given.
A propos d'une conjecture arithmétique sur le groupe de Chow d'une surface rationnelle
A remark on Hilbert's Theorem 92
A Riemann-Hurwitz formula for the Selmer group of an elliptic curve with complex multiplication.
A Tate sequence for global units
An arithmetic proof of Pop`s Theorem concerning Galois groups of function fields over number fields.
Analogues étales de la -tour des corps de classes
Nous construisons un analogue «tordu» de la -tour de corps de classes d’un corps de nombres ( un nombre premier) et étudions ses liens avec la théorie d’Iwasawa. Le résultat principal donne un critère du type Golod et Shafarevich pour que la tour «tordue» soit infinie.
Analogues supérieurs du noyau sauvage
Anticyclotomic main conjectures.
Appendix to Kazuya Kato: A Hasse principle for two dimensional global fields.
Arithmetic and Galois module structure for tame extensions.
Arithmetical Hilbert symbols, distance maps and cohomology
Automorphy for some l-adic lifts of automorphic mod l Galois representations. II
We extend the results of [CHT] by removing the ‘minimal ramification’ condition on the lifts. That is we establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge–Tate numbers), l-adic lifts of certain automorphic mod l Galois representations of any dimension. The main innovation is a new approach to the automorphy of non-minimal lifts which is closer in spirit to the methods of [TW] than to those of [W], which relied on Ihara’s lemma.
Automorphy for some l-adic lifts of automorphic mod l Galois representations
We extend the methods of Wiles and of Taylor and Wiles from GL2 to higher rank unitary groups and establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge–Tate numbers), minimally ramified, l-adic lifts of certain automorphic mod l Galois representations of any dimension. We also make a conjecture about the structure of mod l automorphic forms on definite unitary groups, which would generalise a lemma of Ihara for GL2. Following Wiles’ method we show that this...