Related papers: On $p$-class groups of relative cyclic $p$-extensi…

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…

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…

Let $p$ be a prime number, and $G$ a compact $p$-adic Lie group. We recall that the Iwasawa algebra $\Lambda(G)$ is defined to be the completed group ring of $G$ over the ring of $p$-adic integers. Interesting examples of finitely generated…

Iwasawa made the fundamental discovery that there is a close connection between the ideal class groups of $\mathbb{Z}_{p}$-extensions of cyclotomic fields and the $p$-adic analogue of Riemann's zeta functions…

In this paper, we prove the "local epsilon-isomorphism conjecture" of Fukaya and Kato for a particular class of Galois modules obtained by tensoring a Zp-lattice in a crystalline representation of the Galois group of Qp with a…

We show that the cyclotomic Iwasawa--Greenberg Main Conjecture holds for a large class of modular forms with multiplicative reduction at $p$, extending previous results for the good ordinary case. In fact, the multiplicative case is deduced…

Let $p$ be an odd prime. Denote a Sylow $p$-subgroup of $GL_2(\mathbb{Z}/p^n)$ and $SL_2(\mathbb{Z}/p^n)$ by $S_p(n,GL)$ and $S_p(n,SL)$ respectively. The theory of stable elements tells us that the mod-$p$ cohomology of a finite group is…

We establish a purely algebraic tool for studying the Iwasawa adjoints of some natural Iwasawa modules for $p$-adic Lie group extensions of number fields, by relating them to certain continuous Galois cohomology groups via a spectral…

In this paper, we define a two-variable analogue of Perrin-Riou's p-adic regulator map for the Iwasawa cohomology of a crystalline representation of the absolute Galois group of $\mathbf{Q}_p$, over a Galois extension of $\mathbf{Q}_p$…

Greenberg's conjecture on the stability of $\ell$-class groups in the cyclotomic $\mathbb{Z}_{\ell}$-extension of a real field has been proven for various infinite families of real quadratic fields for the prime $\ell=2$. In this work, we…

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)…

A classical twisting lemma says that given a finitely generated torsion module $M$ over the Iwasawa algebra $\mathbb{Z}_p[[\Gamma ]]$ with $\Gamma \cong \mathbb{Z}_p, \ \exists$ a continuous character $\theta: \Gamma \rightarrow…

We construct the p-adic zeta function for a one-dimensional (as a p-adic Lie extension) non-commutative p-extension of a totally real number field such that the finite part of its Galois group is a pgroup with exponent p. We first calculate…

Let $G$ be an infinite-dimensional real classical group containing the complete unitary group (or complete orthogonal group) as a subgroup. Then $G$ generates a category of double cosets (train) and any unitary representation of $G$ can be…

We prove a general structure theorem for finitely presented torsion modules over a class of commutative rings that need not be Noetherian. As a first application, we then use this result to study the Weil- \'etale cohomology groups of…

Let $G$ be a nilpotent-by-finite compact $p$-adic analytic group for some $p>2$, and $H = \mathbf{FN}_p(G)$ its finite-by-(nilpotent $p$-valuable) radical. Fix a finite field $k$ of characteristic $p$, and write $kG$ for the completed group…

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…

In this paper, we obtain a necessary and sufficient condition for the pseudo-nullity of the $p$-ramified Iwasawa module for $p$-adic Lie extension of totally real fields. It is applied to answer the corresponding question for the minus…

The Taelman class groups associated to Drinfeld modules over function fields serve as an analogue of ideal class groups of number fields. In this paper, we establish an analogue of Iwasawa's asymptotic formula for $\mathbb{Z}_p$-extensions…

We begin a systematic investigation of universal norms for $p$-adic representations in higher rank Iwasawa theory. After establishing the basic properties of the module of higher rank universal norms we construct an Iwasawa-theoretic…