Tamely ramified Hida theory
Let be the Jacobian of the modular curve associated with and the one associated with . We study as a Hecke and Galois-module. We relate a certain matrix of -adic periods to the infinitesimal deformation of the -operator.
Teilkörper relativ abelscher Erweiterungen imaginär-quadratischer Zahlkörper, deren Klassenzahl durch Primteiler des Körpergrades teilbar ist.
The 2-class group of certain biquadratic number fields.
The 2-divisibility of the class number of cyclotomic fields and the Stickelberger ideal.
The Bloch-Kato conjecture on special values of -functions. A survey of known results
This paper contains an overview of the known cases of the Bloch-Kato conjecture. It does not attempt to overview the known cases of the Beilinson conjecture and also excludes the Birch and Swinnerton-Dyer point. The paper starts with a brief review of the formulation of the general conjecture. The final part gives a brief sketch of the proofs in the known cases.
The Brauer-Siegel theorem for algebraic function fields.
The calculation of large units in cyclic cubic fields.
The class number of quadratic fields and the conjectures of Birch and Swinnerton-Dyer
The construction of unramified abelian cubic extensions of a quadratic field
The existence of certain infinite families of imaginary quadratic fields.
The exponent of class groups on congruence function fields
The GL2 main conjecture for elliptic curves without complex multiplication
Let G be a compact p-adic Lie group, with no element of order p, and having a closed normal subgroup H such that G/H is isomorphic to Zp. We prove the existence of a canonical Ore set S* of non-zero divisors in the Iwasawa algebra Λ(G) of G, which seems to be particularly relevant for arithmetic applications. Using localization with respect to S*, we are able to define a characteristic element for every finitely generated Λ(G)-module M which has the property that the quotient of M by its p-primary...
The Hilbert-Kunz Function.
The Image of the Atiyah-Bott Map.
The imaginary bicyclic biquadratic fields with class-number 1.
The integral logarithm in Iwasawa theory : an exercise
Let be an odd prime number and a finite abelian -group. We describe the unit group of (the completion of the localization at of ) as well as the kernel and cokernel of the integral logarithm , which appears in non-commutative Iwasawa theory.
The Iwasawa invariants and the higher -groups associated to real quadratic fields.
The Iwasawa λ-invariants of ℤₚ-extensions of real quadratic fields
1. Introduction. Let k be a totally real number field. Let p be a fixed prime number and ℤₚ the ring of all p-adic integers. We denote by λ=λₚ(k), μ=μₚ(k) and ν=νₚ(k) the Iwasawa invariants of the cyclotomic ℤₚ-extension of k for p (cf. [10]). Then Greenberg’s conjecture states that both λₚ(k) and μₚ(k) always vanish (cf. [8]). In other words, the order of the p-primary part of the ideal class group of kₙ remains bounded as n tends to infinity, where kₙ is the nth layer of . We know by the Ferrero-Washington...
The -rank of the real class group of cyclotomic fields
The least prime ideal.