We give a proof of weak Leopoldt's conjecture a la Perrin-Riou, under some technical condition, for the p-adic realizations of the motive asso- ciated to Hecke characters over an imaginary quadratic fleld K of class number 1, where p... more
We give a proof of weak Leopoldt's conjecture a la Perrin-Riou, under some technical condition, for the p-adic realizations of the motive asso- ciated to Hecke characters over an imaginary quadratic fleld K of class number 1, where p is a prime > 3 where the CM elliptic curve associated to the Hecke character has good reduction at the primes
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We present a collection of results on a conjecture of Jannsen about the p-adic realizations associated to Hecke characters over an imaginary quadratic fleld K of class number 1. The conjecture is easy to check for Galois groups purely of... more
We present a collection of results on a conjecture of Jannsen about the p-adic realizations associated to Hecke characters over an imaginary quadratic fleld K of class number 1. The conjecture is easy to check for Galois groups purely of local type (x1). In x2 we deflne the p-adic realizations associated to Hecke characters over K. We prove the conjecture
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We determine the group structure of the normalizer of Γ0(N) in SL2(ℝ) modulo Γ0(N). These results correct the Atkin–Lehner statement (Atkin and Lehner, 1970, Theorem 8).
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This paper is a brief survey on explicit reciprocity laws of Artin-Hasse-Iwasawa-Wiles type for the Kummer pairing on local fields.
Let $\L$ be a non-noetherian Krull domain which is the inverse limit of noetherian Krull domains $\L_d$ and let $M$ be a finitely generated $\L$-module which is the inverse limit of $\L_d$-modules $M_d\,$. Under certain hypotheses on the... more
Let $\L$ be a non-noetherian Krull domain which is the inverse limit of noetherian Krull domains $\L_d$ and let $M$ be a finitely generated $\L$-module which is the inverse limit of $\L_d$-modules $M_d\,$. Under certain hypotheses on the rings $\L_d$ and on the modules $M_d\,$, we define a pro-characteristic ideal for $M$ in $\L$, which should play the role of the usual characteristic ideals for finitely generated modules over noetherian Krull domains. We apply this to the study of Iwasawa modules (in particular of class groups) in a non-noetherian Iwasawa algebra $\Z_p[[\Gal(\calf/F)]]$, where $F$ is a function field of characteristic $p$ and $\Gal(\calf/F)\simeq\Z_p^\infty$.
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We prove an Iwasawa Main Conjecture for the class group of the $\mathfrak{p}$-cyclotomic extension $\mathcal{F}$ of the function field $\mathbb{F}_q(\theta)$ ($\mathfrak{p}$ is a prime of $\mathbb{F}_q[\theta]\,$), showing that its... more
We prove an Iwasawa Main Conjecture for the class group of the $\mathfrak{p}$-cyclotomic extension $\mathcal{F}$ of the function field $\mathbb{F}_q(\theta)$ ($\mathfrak{p}$ is a prime of $\mathbb{F}_q[\theta]\,$), showing that its Fitting ideal is generated by a Stickelberger element. We use this and a link between the Stickelberger element and a $\mathfrak{p}$-adic $L$-function to prove a close analog of the Ferrero-Washington theorem for $\mathcal{F}$ and to provide informations on the $\mathfrak{p}$-adic valuations of the Bernoulli-Goss numbers $\beta(j)$ (i.e., on the values of the Goss $\zeta$-function at negative integers).
Abstract: We consider $\ mathbb {Z} _p^{\ mathbb {N}} $-extensions $\ mathcal {F} $ of a global function field $ F $ and study various aspects of Iwasawa theory with emphasis on the two main themes already (and still) developed in the... more
Abstract: We consider $\ mathbb {Z} _p^{\ mathbb {N}} $-extensions $\ mathcal {F} $ of a global function field $ F $ and study various aspects of Iwasawa theory with emphasis on the two main themes already (and still) developed in the number fields case as well. When ...
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We determine all modular curves X(N) (with $N\geq 7$) which are hyperelliptic or bielliptic. We make available a proof that the automorphism group of X(N) coincides with the normalizer of $\Gamma(N)$ in $\operatorname{PSL}_2(\mathbb{R})$.