Related papers: Sur la nullit\'e du mu-invariant d'Iwasawa des cor…

We show that the global mixed gauge-gravitational anomaly of the worldvolume theory of the M5-brane vanishes, when the anomaly inflow from the bulk is taken into account. This result extends to the type IIA and heterotic $E_8 \times E_8$…

The paper is withdrawn because the analysis appeared to be incomplete.

For a number field $F$ and an odd prime number $p,$ let $\tilde{F}$ be the compositum of all $\mathbb{Z}_p$-extensions of $F$ and $\tilde{\Lambda}$ the associated Iwasawa algebra. Let $G_{S}(\tilde{F})$ be the Galois group over $\tilde{F}$…

Let $\mathbb{K}$ be an imaginary quadratic field such that $2$ splits into two primes $\mathfrak{p}$ and $\bar{\mathfrak{p}}$. Let $\mathbb{K}_{\infty}$ be the unique $\mathbb{Z}_2$-extension of $\mathbb{K}$ unramified outside…

We present some unexpected examples related to the Kobayashi pseudodistance: For an unramified covering, the vanishing of the Kobayashi pseudodistance on the base does not imply the vanishing on the total space. The vanishing of the…

Building on the construction of big Heegner points in the quaternionic setting, and their relation to special values of Rankin-Selberg $L$-functions, we obtain anticyclotomic analogues of the results of Emerton-Pollack-Weston on the…

This paper has been withdrawn by the author. Much simpler proof of the main result was obtained which led to major changes in the presentation.

Let $p$ be an irregular prime. Let $K=\Q(\zeta)$ be the $p$-cyclotomic field. From Kummer and class field theory, there exist Galois extensions $S/\Q$ of degree $p(p-1)$ such that $S/K$ is a cyclic unramified extension of degree $[S:K]=p$.…

This paper has been withdrawn by the author due to a crucial argument error at p.10.

We give an alternative proof of the mod $p$ vanishing theorem by F.Fang of Seiberg-Witten invariants under a cyclic group action of prime order, and generalize it to the case when $b_1>0$. Although we also use the finite dimensional…

In this paper, for a CM abelian extension $K/k$ of number fields, we propose a conjecture which describes completely the Fitting ideal of the minus part of the Pontryagin dual of the $T$-ray class group of $K$ for a set $T$ of primes as a…

We use Iwasawa theory, at a prime $p$ inert in a quadratic imaginary field $K$, to study the arithmetic properties of mock plectic invariants for elliptic curves of rank two. More precisely, under some minor technical assumptions, we prove…

In this paper, we revise some results on rigidity and vanishing properties obtained by \textit{Cuong et.al} in \cite{CDS24} on $n$-dimensional totally real minimal submanifolds $M$ immersed in complex space forms $\widetilde{M}^n(c)$, for…

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

This paper has been withdrawn as it has been superseded by 0808.2697

The paper has been withdrawn by the author.

We study equivariant Iwasawa theory for two-variable abelian extensions of an imaginary quadratic field. One of the main goals of this paper is to describe the Fitting ideals of Iwasawa modules using $p$-adic $L$-functions. We also provide…

Let $\mathbf{Was}(\mathbb{K})$ denote the group of Washington's cyclotomic units of any abelian number field $\mathbb{K}$. If $\mathbb{K}$ coincides with its genus field in the narrow sense, we give a $\Lambda$-basis of…

We study the behaviour of the Stark conjecture for an abelian extension K/k of totally real number fields as K varies in a cyclotomic Z_p-tower. We consider possible strengthenings of the natural norm-coherence in the tower of putative…

In this paper, we study the module of Euler systems. We determine the ideal of an Iwasawa algebra associated with Euler systems of rank $0$. We also show that the module of higher rank Euler systems for $\mathbb{G}_{m}$ over a totally real…