Related papers: Selmer groups over $\Z_p^d$-extensions

We extend many results on Selmer groups for elliptic curves and modular forms to the non-ordinary setting. More precisely, we study the signed Selmer groups defined using the machinery of Wach modules over $\mathbf{Z}_p$-cyclotomic…

We study the \Lambda-module structure of the Mordell-Weil, Selmer, and Tate-Shafarevich groups of an abelian variety over \mathbb{Z}_p-extensions.

Let $q$ be a prime with $q \equiv 7 \mod 8$, and let $K=\mathbb{Q}(\sqrt{-q})$. Then $2$ splits in $K$, and we write $\mathfrak{p}$ for either of the primes $K$ above $2$. Let $K_\infty$ be the unique $\mathbb{Z}_2$-extension of $K$…

Let $p$ be an odd prime and $K$ an imaginary quadratic field where $p$ splits. Under appropriate hypotheses, Bertolini showed that the Selmer group of a $p$-ordinary elliptic curve over the anticyclotomic $\mathbb Z_p$-extension of $K$ does…

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…

For a given Coleman family of modular forms, we construct a formal modeland prove the existence of a family of Galois representations associated to the Colemanfamily. As an application, we study the variations of Iwasawa $\lambda$- and…

Let $F$ be a global function field of characteristic $p>0$ and $A/F$ an abelian variety. Let $K/F$ be an $\l$-adic Lie extension ($\l\neq p$) unramified outside a finite set of primes $S$ and such that $\Gal(K/F)$ has no elements of order…

Let $E$ be an elliptic curve defined over $\mathbb{Q}$ which has good supersingular reduction at the odd prime $p$. We study the variation of Iwasawa invariants and the $\mathfrak{M}_H(G)$-property for signed Selmer groups over…

Let $\Lambda$ (isomorphic to $\mathbb{Z}_p[[T]]$) denote the usual Iwasawa algebra and $G$ denote the Galois group of a finite Galois extension $L/K$ of totally real fields. When the non-primitive Iwasawa module over the cyclotomic…

We study a geometric analogue of the Iwasawa Main Conjecture for abelian varieties in the two following cases: constant ordinary abelian varieties over $Z_p^d$-extensions of function fields ($d\geq 1$) ramified at a finite set of places,…

Let $A$ be an abelian variety defined over a global function field $F$, and let $p$ be a prime distinct from the characteristic of $F$. Let $F_\infty$ be a $p$-adic Lie extension of $F$ that contains the cyclotomic $\mathbb{Z}_p$-extension…

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…

Let $p$ be an odd prime. Let $f_1$ and $f_2$ be weight-two Hecke eigen-cuspforms with isomorphic residual Galois representations at $p$. Greenberg--Vatsal and Emerton--Pollack--Weston showed that if $p$ is a good ordinary prime for the two…

If $\Lambda $ is an indecomposable, non maximal, symmetric order, then the idealizer of the radical $\Gamma := \Id(J(\Lambda)) = J(\Lambda)^{#} $ is the dual of the radical. If $\Gamma $ is hereditary then $\Lambda $ has a Brauer tree…

In this article we construct characteristic elements for a certain class of Iwasawa modules in noncommutative Iwasawa theory. These elements live in the first K-group K_1(L_T) of the localisation L_T of the Iwasawa algebra L=L(G) of a…

We extend the work of Lai, Longhi, Suzuki, the first two authors and study the change of $\mu$-invariants, with respect to a finite Galois p-extension $K'/K$, of an ordinary abelian variety $A$ over a $\mathbb{Z}_p^d$-extension of global…

In this note, we compare the dual Selmer groups of an abelian variety with that of its dual over certain large Galois field. We give formula which relates the generalized Iwasawa $\mu$-invariants associated with their dual Selmer groups…

This paper is concerned with the study of the fine Selmer group of an abelian variety over a $\mathbb{Z}_p$-extension which is not necessarily cyclotomic. It has been conjectured that these fine Selmer groups are always torsion over…

Let $p$ be a fixed odd prime number, $\mu$ be a Hida family over the Iwasawa algebra of one variable, $\rho_{\mu}$ its Galois representation, $\mathbb{Q}_\infty/\mathbb{Q}$ the $p$-cyclotomic tower and $S$ the variable of the cyclotomic…

Let $A$ be an abelian variety defined over a global function field $F$ of positive characteristic $p$ and let $K/F$ be a $p$-adic Lie extension with Galois group $G$. We provide a formula for the Euler characteristic $\chi(G,Sel_A(K)_p)$ of…