Selberg zeta functions with virtual characters and the class number
Selmer groups and Heegner points in anticyclotomic -extensions
Selmer groups for elliptic curves in -extensions of function fields of characteristic
Let be a function field of characteristic , a -extension (for some prime ) and a non-isotrivial elliptic curve. We study the behaviour of the -parts of the Selmer groups ( any prime) in the subextensions of via appropriate versions of Mazur’s Control Theorem. As a consequence we prove that the limit of the Selmer groups is a cofinitely generated (in some cases cotorsion) module over the Iwasawa algebra of .
Semi-local units modulo Gauss sums.
Several-variable -adic families of Siegel-Hilbert cusp eigensystems and their Galois representations
Siegel Modular Forms of Degree Two: Hecke Eigenforms.
Sieve methods and class-number probelms. II.
Sieve methods and class-number problems. I.
Signature des unités cyclotomiques et parité du nombre de classes des extensions cycliques de de degré premier impair
Signature des unités cyclotomiques et parité du nombre de classes des extensions cycliques de de degré premier impair
Si est une extension abélienne de de degré impair, l’étude du 2-groupe des classes (au sens ordinaire) de (et même celle de la parité du nombre de classes de ) est non triviale, et les algorithmes connus ne dépassent guère le cas .L’expression analytique de s’interprète à l’aide d’indices convenables de groupes d’unités cyclotomiques (Hasse et Leopoldt) ; ce dernier point de vue permet une caractérisation de la parité de , en fonction de l’existence d’unités cyclotomiques totalement...
Signed Selmer groups over -adic Lie extensions
Let be an elliptic curve over with good supersingular reduction at a prime and . We generalise the definition of Kobayashi’s plus/minus Selmer groups over to -adic Lie extensions of containing , using the theory of -modules and Berger’s comparison isomorphisms. We show that these Selmer groups can be equally described using Kobayashi’s conditions via the theory of overconvergent power series. Moreover, we show that such an approach gives the usual Selmer groups in the ordinary case....
Singular Moduli, Modular Polynomials, and the Index of the Closure of Z [j (...)] in Q (j(...)).
Small values of zeta-functions of quadratic fields.
Some Analytic Bounds for Zeta Functions and Class Numbers.
Some non-semi-simple Iwasawa modules
Some Recent Developments in three Classical Problems of Number Theory.
Some remarks on L-functions and class numbers
Sommes de Gauss et structure galoisienne des anneaux d'entiers
Stabilization in non-abelian Iwasawa theory
Let K/k be a ℤₚ-extension of a number field k, and denote by kₙ its layers. We prove some stabilization properties for the orders and the p-ranks of the higher Iwasawa modules arising from the lower central series of the Galois group of the maximal unramified pro-p-extension of K (resp. of the kₙ).
Stickelberger elements in function fields