Yuan Liu

activity

20142024

most citedA predicted distribution for Galois groups of maximal unramified extensions

8 citations · 27 across the 15 of their papers we have counts for

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math.NT2022

On the $p$ -rank of class groups of $p$ -extensions

Yuan Liu

We prove a local-global principle for the embedding problems of global fields with restricted ramification. By this local-global principle, for a global field $k$ , we use only the…

math.NT2022★ 1 cited

Non-abelian Cohen--Lenstra Heuristics in the presence of roots of unity

Yuan Liu

For a Galois extension $K / F_{q} (t)$ of Galois group $Γ$ with $g cd (q, ∣Γ∣) = 1$ , we define an invariant $ω_{K}$ , and show that it determines the Weil pairing of the curve corresp…

math.NT2020

Tamely Ramified Covers of the Projective Line with Alternating and Symmetric Monodromy

Renee Bell, Jeremy Booher, William Y. Chen +1

Let $k$ be an algebraically closed field of characteristic $p$ and let $X$ the projective line over $k$ with three points removed. We investigate which finite groups $G$ can arise…

math.NT2020

Presentations of Galois groups of maximal extensions with restricted ramification

Yuan Liu

Motivated by the work of Lubotzky, we use Galois cohomology to study the difference between the number of generators and the minimal number of relations in a presentation of the Ga…

math.NT2020★ 5 cited

Generalized Bockstein maps and Massey products

Yeuk Hay Joshua Lam, Yuan Liu, Romyar Sharifi +2

Given a profinite group G of finite p-cohomological dimension and a pro-p quotient H of G by a closed normal subgroup N, we study the filtration on the Iwasawa cohomology of N by p…

math.NT2019★ 8 cited

A predicted distribution for Galois groups of maximal unramified extensions

Yuan Liu, Melanie Matchett Wood, David Zureick-Brown

We consider the distribution of the Galois groups $Gal (K^{un} / K)$ of maximal unramified extensions as $K$ ranges over $Γ$ -extensions of $Q$ o…

math.NT2018

On the level of modular curves that give rise to isolated $j$ -invariants

Abbey Bourdon, Ozlem Ejder, Yuan Liu +2

We say a closed point $x$ on a curve $C$ is sporadic if $C$ has only finitely many closed points of degree at most $deg (x)$ and that $x$ is isolated if it is not in…

math.NT2017

The Realizability Problem with Inertia Conditions

Yuan Liu

In this paper, we consider the inverse Galois problem with described inertia behavior. For a finite group $G$ , one of its subgroups $I$ and a prime integer $p$ , we ask whether or n…

On the p-rank of class groups of p-extensions

Non-abelian Cohen--Lenstra Heuristics in the presence of roots of unity

Tamely Ramified Covers of the Projective Line with Alternating and Symmetric Monodromy

Presentations of Galois groups of maximal extensions with restricted ramification

Generalized Bockstein maps and Massey products

A predicted distribution for Galois groups of maximal unramified extensions

On the level of modular curves that give rise to isolated j-invariants

The Realizability Problem with Inertia Conditions

On the $p$ -rank of class groups of $p$ -extensions

On the level of modular curves that give rise to isolated $j$ -invariants