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Ben Forrás

Publications and source records attributed to Ben Forrás.

7 recordsLinked to original sources
arXiv2026

Iwasawa theory of CM elliptic curves at potentially supersingular primes

We develop a plus and minus Iwasawa theory for CM elliptic curves with potentially supersingular reduction at a prime $p\ge5$. We construct local points that satisfy suitable "jumping trace" relations using the Honda--Demchenko theory applied to height-two formal groups over local fields with small ramification degree. These local points allow us to study plus and minus Selmer groups of CM elliptic curves over the cyclotomic $\mathbb{Z}_p$-extension, to construct the corresponding plus and minus $p$-adic $L$-functions, and to prove an Iwasawa main conjecture relating these objects. As an application, we obtain asymptotic growth formulae for the $p$-primary part of the Tate--Shafarevich groups.

math.NT↗
arXiv2026

Class Number Relations in Abelian Extensions of Global Fields

Consider a finite abelian extension $K/k$ of global fields with Galois group $G$. We study the rank-one component of the generalized Stickelberger module associated with $K/k$ and a finite set $S$ of places of $k$. Under explicit splitting conditions on $S$, we compute generalized indices of this module with respect to the torsion-free part of the $S$-unit group of $K$. We also obtain $p$-primary refinements which include the non-semisimple case $p\mid |G|$. As applications, we derive divisibility relations between the $S$-class numbers of $K$ and $k$, both for number fields and for function fields.

math.NT↗
arXiv2026

On the Wedderburn decomposition of the total ring of quotients of certain Iwasawa algebras II

Let $\mathcal G\simeq H\rtimesΓ$ be the semidirect product of a finite group $H$ and $Γ\simeq\mathbb Z_p$. Let $ F/\mathbb Q_p$ be a finite extension with ring of integers $\mathcal O_F$. Then the total ring of quotients $\mathcal Q^F(\mathcal G)$ of the completed group ring $\mathcal O_F[[\mathcal G]]$ is semisimple artinian. We determine its Wedderburn decomposition in full generality in terms of the Wedderburn decomposition of the group ring $ F[H]$. Such a description was previously available only for those simple components for which a certain associated field extension is totally ramified.

math.RA↗
arXiv2025

On the Wedderburn decomposition of the total ring of quotients of certain Iwasawa algebras

Let $\mathcal G\simeq H\rtimesΓ$ be the semidirect product of a finite group $H$ and $Γ\simeq\mathbb Z_p$. Let $F/\mathbb Q_p$ be a finite extension with ring of integers $\mathcal O_F$. Then the total ring of quotients $\mathcal Q^F(\mathcal G)$ of the completed group ring $\mathcal O_{F}[[\mathcal G]]$ is a semisimple ring. We determine its Wedderburn decomposition under a ramification hypothesis by relating it to the Wedderburn decomposition of the group ring $F[H]$.

math.RA↗
arXiv2025

Graduated orders over completed group rings and conductor formulæ

We study graduated orders over completed group rings of $1$-dimensional admissible $p$-adic Lie groups, and verify the equivariant $p$-adic Artin conjecture for such orders. Following Jacobinski and Plesken, we obtain a formula for the conductor of a graduated order into a self-dual order. We also refine Nickel's central conductor formula by determining a hitherto implicit exponent $r_χ$.

math.RA↗
arXiv2025

An equivariant $p$-adic Artin conjecture

We formulate an equivariant version of Greenberg's $p$-adic Artin conjecture for smoothed equivariant $p$-adic Artin $L$-functions in the context of an arbitrary one-dimensional admissible $p$-adic Lie extension of a totally real number field. Using results of the author on the Wedderburn decomposition of the total ring of quotients of the Iwasawa algebra $Λ(\mathcal G)$, we deduce validity of the conjecture in several interesting cases.

math.NT↗