相关论文: Malle's Conjecture for $S_n\times A$ for $n = 3,4,…

We prove Malle's conjecture for $G \times A$, with $G=S_3, S_4, S_5$ and $A$ an abelian group. This builds upon work of the fourth author, who proved this result with restrictions on the primes dividing $A$.

Let $G$ be a finite nilpotent group and $n\in \{3,4, 5\}$. Consider $S_n\times G$ as a subgroup of $S_n\times S_{|G|}\subset S_{n|G|}$, where $G$ embeds into the second factor of $S_n\times S_{|G|}$ via the regular representation. Over any…

We give counterexamples for the modification on Malle's Conjecture given by T\"urkelli. T\"urkelli's modification on Malle's conjecture is inspired by an analogue of Malle's conjecture over a function field. As a consequence, our…

We develop an abstract framework for studying the strong form of Malle's conjecture for nilpotent groups $G$ in their regular representation. This framework is then used to prove the strong form of Malle's conjecture for any nilpotent group…

We study Malle's conjecture for the group $C_2 \wr H$ where $H$ is a permutation group. Malle's conjecture for this case was proved by J\"urgen Kl\"uners in \cite{arXiv:1108.5597} under mild conditions for $H$. In this article, we provide…

In this paper, we use inductive methods similar to those employed in a 2025 paper by Alberts, Lemke Oliver, Wang and Wood in order to prove many new cases of the Twisted Malle's Conjecture. Previously, this conjecture had only been proven…

Let $N_d(G,X)$ denote the number of degree $d$ extensions of $\mathbb{Q}$ with Galois closure $G$ and $|\Delta_K|\leq X$. Malle's conjecture predicts an asymptotic of the form $N_d(G,X)\sim CX^{\alpha}(\log X)^\beta$. Previously, Kl\"uners…

For a fixed finite solvable group $G$ and number field $K$, we prove an upper bound for the number of $G$-extensions $L/K$ with restricted local behavior (at infinitely many places) and ${\rm inv}(L/K)<X$ for a general invariant $"{\rm…

We describe the relations among the $\ell$-torsion conjecture, a conjecture of Malle giving an upper bound for the number of extensions, and the discriminant multiplicity conjecture. We prove that the latter two conjectures are equivalent…

A conjecture of Malle predicts the quantity of number fields with bounded discriminant of given Galois group. We present a lower bound matching this in the case of quartic fields with Galois group $A_4$.

The Malle-Navarro conjecture relates central block theoretic invariants in two inequalities. In this paper, we prove the conjecture for the 2-blocks and the unipotent 3-blocks of the general linear and unitary groups in non-defining…

In this note we give a counter example to a conjecture of Malle which predicts the asymptotic behaviour of the counting functions for field extensions with given Galois group and bounded discriminant.

Foulkes' conjecture has several generalisations due to Doran, Abdesselam--Chipalkatti, Bergeron, and Troyka. For the special linear Lie algebra $\mathfrak{sl}_2(\mathbb{C})$, these assert that given $a \le c \le d \le b$ with $ab=cd$, the…

We study certain unitary CM fields whose Galois closure has Galois group $\operatorname{PSL}_2(\mathbb{F}_q) \times \mathbb{Z}/2\mathbb{Z}$. After investigating the CM types of these fields, we turn towards Colmez's conjectural formula on…

In the representation theory of finite groups, Brou\'e's abelian defect group conjecture says that for any prime p if a p-block A of a finite group G has an abelian defect group P, then A and its Brauer corresponding block B of the…

We study the indecomposable summands of the permutation module obtained by inducing the trivial $\mathbb{F}(S_a\wr S_n)$-module to the full symmetric group $S_{an}$ for any field $\mathbb{F}$ of odd prime characteristic $p$ such that…

In the representation theory of finite groups, there is a well-known and important conjecture due to M. Brou\'e. He conjectures that, for any prime p, if a p-block A of a finite group G has an abelian defect group P, then A and its Brauer…

We compute the asymptotic number of octic number fields whose Galois groups over $\mathbb Q$ are isomorphic to $D_4$, the symmetries of a square, when ordering such fields by their absolute discriminants. In particular, we verify the strong…

In representation theory of finite groups, there is a well-known and important conjecture due to M. Brou\'e. He conjectures that, for any prime $p$, if a $p$-block $A$ of a finite group $G$ has an abelian defect group $P$, then $A$ and its…

We define invariants $\operatorname{inv}_1,\dots,\operatorname{inv}_m$ of Galois extensions of number fields with a fixed Galois group. Then, we propose a heuristic in the spirit of Malle's conjecture which asymptotically predicts the…