Related papers: On capitulations and pseudo-null submodules in cer…

Kurihara established a refinement of the minus-part of the Iwasawa main conjecture for totally real number fields using the higher Fitting ideals. In this paper, we study the higher Fitting ideals of the plus-part of the Iwasawa module…

Let p be an odd prime. Suppose that E is a modular elliptic curve/Q with good ordinary reduction at p. Let Q_{oo} denote the cyclotomic Z_p-extension of Q. It is conjectured that Sel_E(Q_{oo}) is a cotorsion Lambda-module and that its…

In this note, we investigate the p-adic behavior of Weil numbers in the cyclotomic $\mathbb Z\_p$-extension of $\mathbb Q(\zeta\_p).$ We determlne the characteristic ideal of the quotient of semi-local units by Weil numbers in terms of the…

Let $\ell$ and $p$ be distinct primes, and let $\G$ be an abelian pro-$p$-group. We study the structure of the algebra $\L:=\Z_\ell[[\G]]$ and of $\L$-modules. The algebra $\L$ turns out to be a direct product of copies of ring of integers…

The Iwasawa theory of CM fields has traditionally concerned Iwasawa modules that are abelian pro-p Galois groups with ramification allowed at a maximal set of primes over p such that the module is torsion. A main conjecture for such an…

In this paper, we relate three objects. The first is a particular value of a cup product in the cohomology of the Galois group of the maximal unramified outside p extension of a cyclotomic field containing the pth roots of unity. The second…

Let $K_\infty/K$ be a uniform $p$-adic Lie extension. We compare several arithmetic invariants of Iwasawa modules of ideal class groups on the one side and fine Selmer groups of abelian varieties on the other side. If $K_\infty$ contains…

We present certain results on the Iwasawa theory of an abelian variety with potentially good ordinary reduction at all primes above $p$. These are then applied to study Diophantine stability and integally Diophantine extensions. Along the…

The main conjectures in Iwasawa theory predict the relationship between the Iwasawa modules and the $p$-adic $L$-functions. Using a certain proved formulation of the main conjecture, Greither and Kurihara described explicitly the (initial)…

We first study some families of maximal real subfields of cyclotomic fields with even class number, and then explore the implications of large plus class numbers of cyclotomic fields. We also discuss capitulation of the minus part and the…

We study a geometric analogue of the Iwasawa Main Conjecture for constant ordinary abelian varieties over $\ZZ_p^d$-extensions of function fields ramifying at a finite set of places.

Let $k_\infty$ be the cyclotomic $\mathbb{Z}_p$-extension field of an algebraic number field $k$. Moreover, we take a $\mathbb{Z}_p$-extension $K_\infty$ over $k_\infty$. In this paper, we study the behavior of the $p$-part of the class…

Let $p$ be an odd prime and $F_{\infty,\infty}$ a $p$-adic Lie extension of a number field $F$ with Galois group isomorphic to $\mathbb{Z}_p^r\rtimes\mathbb{Z}_p$, $r\geq 1$. Under certain assumptions, we prove an asymptotic formula for the…

In this paper, we study the module-theoretic structure of classical Iwasawa modules. More precisely, for a finite abelian $p$-extension $K/k$ of totally real fields and the cyclotomic $\mathbb{Z}_p$-extension $K_{\infty}/K$, we consider…

For an odd prime number $p$, we study the number of generators of the unramified Iwasawa modules of the maximal multiple $\mathbb{Z}_p$-extensions over Iwasawa algebra. In a previous paper of the authors, under several assumptions for an…

We introduce a new ideal {\mathfrak D} of the p-adic Galois group-ring associated to a real abelian field and a related ideal {\mathfrak J} for imaginary abelian fields. Both result from an equivariant, Kummer-type pairing applied to Stark…

This is the first in a series of articles where we will study the Iwasawa theory of an elliptic modular form f along the anticyclotomic Zp-tower of an imaginary quadratic field K where the prime p splits completely. Our goal in this portion…

Let G be a nilpotent p-valuable (compact p-adic Lie) group. There is an ongoing investigation into the prime ideals of its completed group algebra (Iwasawa algebra), and there remains an open conjecture that they can all be proved to have a…

In our previous work, by using Kolyvagin derivatives of elliptic units, we constructed ideals C_i of the Iwasawa algebra, and proved that the ideals C_i become "upper bounds" of the higher Fitting ideals of the one and two variable p-adic…

We discuss the formalism of Iwasawa theory descent in the setting of the localized K_1-groups of Fukaya and Kato. We then prove interpolation formulas for the `leading terms' of the global Zeta isomorphisms that are associated to certain…