Cheng Meng

activity

20212026

collaborators

9 papers

math.AC2026

Hilbert-Kunz multiplicity of quadrics decreases

Cheng Meng

In this paper we prove that the Green ring of $Z / p^{e} Z$ is the $e$ -fold tensor product of the Green ring of $Z / p Z$ , and this isomorphism is given…

math.RT2026

Asymptotic behavior of modular representations over abelian $p$ -groups

Cheng Meng

In this paper, we prove some results on the asymptotic behavior arising in modular representation theory over abelian $p$ -groups. First, we embed the representation ring of a cycli…

math.AC2025

Finiteness and infiniteness of gradings of Noetherian rings

Cheng Meng

In this paper we show that for a torsion-free abelian group $G$ , $rank_{Z} G < \infty$ if and only if there exists a Noetherian $G$ -graded ring $R$ such that the…

math.AC2025

Explicit Stillman bounds for all degrees

Giulio Caviglia, Yihui Liang, Cheng Meng

In 2016 Ananyan and Hochster proved Stillman's conjecture by showing the existence of a uniform upper bound on the length of an $R_{η}$ -sequence containing fixed $n$ forms of degree…

math.AC2025

Limits of $F$ -invariants and Riemann-Stieltjes integral

Cheng Meng

This paper proves several results on $F$ -invariants of Fermat hypersurfaces, including the proof of an inequality on the Hilbert-Kunz multiplicity of Fermat quadric hypersurfaces c…

math.AC2025

Restrictions on Hilbert coefficients give depths of graded domains

Cheng Meng

In this paper, we prove that if $P$ is a homogeneous prime ideal inside a standard graded polynomial ring $S$ with $dim (S / P) = d$ , and for $s \leq d$ , adjoining $s$ general linear f…

math.AC2024

Asymptotic colengths for families of ideals: an analytic approach

Sudipta Das, Cheng Meng

This article focuses on the existence of asymptotic colengths for families of $\fm_{R}$-primary ideals in a Noetherian local ring $(R,\fm)$. In any characteristic, we generalize gr…

math.AC2023

$h$ -function, Hilbert-Kunz density function and Frobenius-Poincaré function

Cheng Meng, Alapan Mukhopadhyay

Given ideals $I, J$ of a noetherian local ring $(R, m)$ such that $I + J$ is $m$ -primary and a finitely generated $R$ -module $M$ , we associate an invariant of $(M,…

math.AC2021

Strongly Lech-independent ideals and Lech's conjecture

Cheng Meng

We introduce the notion of strongly Lech-independent ideals as a generalization of Lech-independent ideals defined by Lech and Hanes, and use this notion to derive inequalities on…

Hilbert-Kunz multiplicity of quadrics decreases

Asymptotic behavior of modular representations over abelian p-groups

Finiteness and infiniteness of gradings of Noetherian rings

Explicit Stillman bounds for all degrees

Limits of F-invariants and Riemann-Stieltjes integral

Restrictions on Hilbert coefficients give depths of graded domains

Asymptotic colengths for families of ideals: an analytic approach

h-function, Hilbert-Kunz density function and Frobenius-Poincaré function

Strongly Lech-independent ideals and Lech's conjecture

Asymptotic behavior of modular representations over abelian $p$ -groups

Limits of $F$ -invariants and Riemann-Stieltjes integral

$h$ -function, Hilbert-Kunz density function and Frobenius-Poincaré function