Yuan Liu

collaborators

6 papers

math.NT2025

Statistics of bad parts of class groups

Peter Koymans, Yuan Liu

Let $p$ be an odd prime. We give a formula for the bad part of $p$ -class groups that is valid for $100%$ of the abelian $p$ -extensions when ordered by product of ramified primes.

math.GT2025

The applications of Bieri-Neumann-Strebel invariant on KÃ¤hler groups

Yuan Liu

We give several applications of the Bieri-Neumann-Strebel invariant on KÃ¤hler groups. Specifically, we provide simpler proof of the Napier-Ramachandran theorem on the HNN extensio…

math.NT2025

The imaginary case of the nonabelian Cohen--Lenstra heuristics

Yuan Liu, Ken Willyard

For a finite group $I^$ , we study the distribution of the Galois group $G_{\emptyset}^{#} (K)$ of the maximal unramified extension of $K$ that is split completely at $\infty$ and h…

math.GT2025

Bieri-Neumann-Strebel-Renz invariants and tropical varieties of integral homology jump loci

Yongqiang Liu, Yuan Liu

Papadima and Suciu studied the relationship between the Bieri-Neumann-Strebel-Renz (short as BNSR) invariants of spaces and the homology jump loci of rank one local systems. Recent…

math.NT2024

On the Distribution of Class Groups of Abelian Extensions

Yuan Liu

Given a finite abelian group $I^$ , we study the distribution of the $p$ -part of the class group $Cl (K)$ as $K$ varies over Galois extensions of $Q$ or $\mat…

math.CV2024

On the holomorphic convexity of nilpotent coverings over compact KÃ¤hler surfaces

Yuan Liu

We prove that any nilpotent regular covering over a compact KÃ¤hler surface is holomorphically convex if it does not have two ends. Furthermore, we show that the Malcev covering of…