(1)ERRATA: THE 2-SELMER GROUP OF A NUMBER FIELD AND HEURISTICS FOR NARROW CLASS GROUPS AND SIGNATURE RANKS OF UNITS DAVID S

If a number field F contains the 2`-th roots of unity then the wild kernel of F and its logarithmic `-class group have the

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In the next three subsections we describe how this construction works for cy- clotomic fields, for CM fields and for other more general fields. To simplify the notations, we only

We give the coefficients of the irreducible characters of the symmetric group that contribute to the number of cycles of a permutation, considered as a class function of

In this paper we define relative congruence ideals for various automorphic symmetric powers Symm m f of a Hida family f over Q in big ordinary Hecke algebras for symplectic and

To conclude, we will show that the behavior, in K/k, of the finite torsion groups T n of p-ramification theory (as “dual” invariants of p-class groups) gives much strongly

Then we show, in this context, that Kida’s formula on lambda invariants is valid for the p-ranks if and only if the p-class group of K is reduced to the group of ambiguous

§1.3 we develop the basics of the theory of Minkowski units and show, using the Gras- Munnier Theorem 1.1, that the existence of a Minkowski unit in some number field F in the tower K