Related papers: Capitulation kernels of class groups over Z_p^d-ex…

For a real quadratic field $K=\mathbb{Q}(\sqrt{D})$, let $K_{\infty}$ denote the cyclotomic $\mathbb{Z}_{p}$-extension of $K$. Greenberg conjectured that the corresponding Iwasawa module $X_{\infty}$ is finite. Building on the work of…

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…

Let $p$ be an odd prime number and $k$ an imaginary quadratic field in which $p$ splits. In this paper, we consider a weak form of Greenberg's generalized conjecture for $p$ and $k$, which states that the non-trivial Iwasawa module of the…

A construction due to Darmon--Rotger gives rise to generalised Kato classes $\kappa_p(E)$ in the $p$-adic Selmer group ${\rm Sel}(\mathbf{Q},V_pE)$ of elliptic curves $E/\mathbf{Q}$ of positive even analytic rank, where $p>3$ is any prime…

We show a classification method for finite groupoids and discuss the cardinality of cosets and its relation with the index. We prove a generalization of the Lagrange's Theorem and establish a Sylow theory for groupoids.

In this paper we prove the $\pm$-main conjecture of Iwasawa theory formulated by Kobayashi for elliptic curves with supersingular reduction at an odd prime $p$ such that $a_p=0$, using a key new observation that it can be reduced to another…

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 and $f$ be a nearly ordinary Hilbert modular Hecke eigenform defined over a totally real field $F$. Let $\mathbb{I}$ be an irreducible component of the universal nearly ordinary or locally cyclotomic deformation of…

We study minimal and toroidal compactifications of $p$-integral models of Hilbert modular varieties. We review the theory in the setting of Iwahori level at primes over $p$, and extend it to certain finer level structures. We also prove…

We express the set of representations from a cyclic $p$-group to a connected $p$-compact group in terms of the associated reflection group and compute its cardinality for each exotic $p$-compact group.

Let l be an odd prime and K/k a Galois extension of totally real number fields with Galois group G such that K/k_\infty and k/Q are finite. We give a full description of the algebraic structure of the semisimple algebra QG=Quot(\Lambda G)…

We revisit the theory of Ihara $L$-functions in the context initially studied by Bass and Hashimoto and more recently by Zakharov. In particular, we study if the Artin formalism is satisfied by these $L$-functions. As an application, we…

We characterize the group property of being with infinite conjugacy classes (or icc, in which all conjugacy classes beside 1 are infinite) for extensions of some specific groups ; namely extensions of abelian, centerless, icc, or word…

We set up a general framework to study Tate cohomology groups of Galois modules along $\mathbb{Z}_p$-extensions of number fields. Under suitable assumptions on the Galois modules, we establish the existence of a five-term exact sequence in…

We prove a local-global principle for the embedding problems of global fields with restricted ramification. By this local-global principle, for a global field $k$, we use only the local information to give a presentation of the maximal…

We reveal a new and refined application of (a weaker statement than) the Iwasawa main conjecture for elliptic curves to the structure of Selmer groups of elliptic curves of arbitrary rank. For a large class of elliptic curves, we obtain the…

For primes $q \equiv 7 \mod 16$, the present manuscript shows that elementary methods enable one to prove surprisingly strong results about the Iwasawa theory of the Gross family of elliptic curves with complex multiplication by the ring of…

We prove the vanishing of $SK_1(\Zp\ps{G})$ when $G$ is either $\Zp^n\rtimes\Zp$ or a Heisenberg pro-$p$ group.

Our primary goal in this article is to study the Iwasawa theory for semi-ordinary families of automorphic forms on $\mathrm{GL}_2\times\mathrm{Res}_{K/\mathbb{Q}}\mathrm{GL}_1$, where $K$ is an imaginary quadratic field where the prime $p$…

Let $p$ be a prime number such that $p\equiv 1$ mod $8$ and $i=\sqrt{-1}$. Let $\mathbf{k}=\mathbb{Q}(\sqrt{2p}, i)$, $\mathbf{k}_1^{(2)}$ be the Hilbert $2$-class field of $\mathbf{k}$, $\mathbf{k}_2^{(2)}$ be the Hilbert $2$-class field…