arXiv subjects

Zugan Xing

Publications and source records attributed to Zugan Xing.

3 recordsLinked to original sources

arXiv2026

Multiplicator freeness for restricted-ramification Galois groups over global function fields

Let $K$ be a global function field with full constant field $\mathbb{F}_q$, let $T$ be a finite set of finite places, and let $\infty$ be a distinguished place. We study the maximal pro-$\ell$ extension of $K$ which is unramified outside $T$ and in which $\infty$ splits completely. Using factorisation results for $\ell$-primary idele class characters, we prove that its Galois group is multiplicator-free if $\ell \nmid q - 1$ or $T \neq \varnothing$. In particular, if $T \neq \varnothing$, the conclusion holds for every prime $\ell$.

math.NT↗

arXiv2024

On the Finiteness and Structure of Galois Groups of Tamely ramified pro-p Extensions of Imaginary Quadratic Fields

For a prime p, we study the Galois groups of maximal pro-$p$ extensions of imaginary quadratic fields unramified outside a finite set $S$, where $S$ consists of one or two finite places not lying above $p$. When $p$ is odd, we give explicit presentations of these Galois groups under certain conditions. As an application, we determine the structure of the maximal pro-$3$ extension of $\mathbb{Q}(i)$ unramified outside two specific finite places.

math.NT↗

arXiv2024

Infinite class field tower with small root discriminant

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 infinite $p$-class field tower when $p=3, 5, 7$.

math.NT↗