Related papers: New number fields with known p-class tower

Graded-division algebras are building blocks in the theory of finite-dimensional associative algebras graded by a group G. If G is abelian, they can be described, using a loop construction, in terms of central simple graded-division…

We examine the ramification groups of finite Galois extensions over complete discrete valuation fields of equal characteristic $p>0$. Brylinski (1983) calculated the ramification groups in the case where the Galois groups are abelian. We…

We consider p-extensions of number fields such that the filtration of the Galois group by higher ramification groups is of prescribed finite length. We extend well-known properties of tame extensions to this more general setting; for…

Fix K a p-adic field and denote by G_K its absolute Galois group. Let K_infty be the extension of K obtained by adding (p^n)-th roots of a fixed uniformizer, and G_\infty its absolute Galois group. In this article, we define a class of…

Let $K/\Q$ be a cyclic extension of number fields with Galois group $G$. We study the ideal classes of primes $\mathfrak{p}$ of $K$ of residue degree bigger than one in the class group of $K$. In particular, we explore such extensions…

We construct extensions of the field of rational numbers with the Galois group G_2(F_p) by reducing p-adic representations attached to automorphic representations.

For given rational prime number $p$ consider the tower of finite extensions of fields $K_0/\mathbb{Q}_p,$ $K/K_0, L/K, M/L$, where $K/K_0$ is unramified and $M/L$ is a Galois extension with Galois group $G$. Suppose one dimensional Honda…

We prove that the $p^\infty$-torsion of the transcendental Brauer group of an abelian variety over a finitely generated field of characteristic $p>0$ is bounded. This answers a (variant of a) question asked by Skorobogatov and Zarhin for…

In 2020, Alabdali and Byott described the Hopf-Galois structures arising on Galois field extensions of squarefree degree. Extending to squarefree separable, but not necessarily normal, extensions $L/K$ is a natural next step. One must…

We construct an infinite family of imaginary quadratic number fields with 2-class groups of type (2,2,2) whose Hilbert 2-class fields are finite.

Using the theory of pro-p groups and relative Poincar\'{e} duality, we define a type of cobordism category well suited to arithmetic topology. We completely classify topological quantum field theories on these two-dimensional versions of…

We study the groups in the unit filtration of a finite abelian extension K of the field of p-adic numbers. We determine explicit generators of these groups as modules over the pro-p group ring of the Galois group of K over the p-adic…

Let $G$ be a Frobenius group with an abelian Frobenius kernel $F$ and let $k$ be a finite extension of $\mathbb{Q}$. We obtain an upper bound for the number of degree $|F|$ algebraic extensions $K/k$ with Galois group $G$ with the norm of…

In this paper we give an elementary proof of results on the structure of 4-class groups of real quadratic number fields originally due to A. Scholz. In a second (and independent) section we strengthen C. Maire's result that the 2-class…

Let $A$ be a finite commutative nilpotent $\mathbb{F}_p$-algebra structure on $G$, an elementary abelian group of order $p^n$. If $K/k$ is a Galois extension of fields with Galois group $G$ and $A^p = 0$, then corresponding to $A$ is an…

For fields F of characteristic not p containing a primitive $p$th root of unity, we determine the Galois module structure of the group of $p$th-power classes of K for all cyclic extensions K/F of degree p.

Let $p$ be an odd prime and $F_{\infty}$ a $p$-adic Lie extension of a number field $F$ with Galois group $G$. Suppose that $G$ is a compact pro-$p$ $p$-adic Lie group with no torsion and that it contains a closed normal subgroup $H$ such…

Let $K$ be a number field or a function field. Let $f\in K(x)$ be a rational function of degree $d\geq 2$, and let $\beta\in\mathbb{P}^1(K)$. For all $n\in\mathbb{N}\cup\{\infty\}$, the Galois groups…

We generalize Schoof's theorem in 1986 and apply this to construct a class of Kummer extensions of the cyclotomic fields with infinite class tower. As an application, we give some number fields with a small root discriminant, which has an…

We show that if F is the rational numbers or a multiquadratic number field, p is 2,3, or 5, and K/F is a Galois extension of degree a power of p, then for elliptic curves E/Q ordered by height, the average dimension of the p-Selmer groups…