arXiv subjects

Zhenmou Liu

Publications and source records attributed to Zhenmou Liu.

4 recordsLinked to original sources

arXiv2026

Geometric Detection and Finiteness of Crystalline Local Systems

We prove a geometric detection theorem for crystalline local systems on the generic fiber of a smooth proper scheme over the ring of integers of a $p$-adic field. The special-fiber crystalline realization detects geometric absolute irreducibility and, modulo constant rank-one twists, determines the restriction to the geometric fundamental group. The main ingredient is a determinant argument combining a finite-order rank-one reduction, period comparison, and the Plücker embedding. As an application, using Abe--Esnault's finiteness theorem and finiteness of stable lattices, we prove finiteness, up to arithmetic character twists, of geometrically absolutely irreducible crystalline local systems of fixed rank. Coefficients may lie in any fixed finite extension of $\mathbb Q_p$, and no bound on the Hodge--Tate weights is imposed.

math.AG↗

arXiv2026

Logarithmic Crystalline Representations

In 1989, Faltings proved the comparison theorem between étale cohomology and crystalline cohomology by studying Fontaine-Faltings modules and crystalline representations. In his paper, he mentioned these modules and representations can be extended to the logarithmic context, but without detail. This note aims to explicitly present the construction of logarithmic Fontaine-Faltings modules and logarithmic crystalline representations.

math.AG↗

arXiv2025

Parabolic Crystalline Representations

The theory of crystalline representations was established by Fontaine and Laffaille, Faltings, and others. In this paper, we develop a parabolic version of this theory. The key point is the construction of the parabolic version of Fontaine-Faltings modules and Faltings' $\mathbb D$-functor. The theory of Higgs-de Rham flows can be used to efficiently construct crystalline representations. We have established a parabolic version and utilized it to construct infinitely many crystalline representations. The twisted versions discussed in Sun, Yang, and Zuo's work can be seen as a special case, where the parabolic weights are equal at every infinity point.

math.AG↗

arXiv2024

Privacy-preserving Pseudonym Schemes for Personalized 3D Avatars in Mobile Social Metaverses

The emergence of mobile social metaverses, a novel paradigm bridging physical and virtual realms, has led to the widespread adoption of avatars as digital representations for Social Metaverse Users (SMUs) within virtual spaces. Equipped with immersive devices, SMUs leverage Edge Servers (ESs) to deploy their avatars and engage with other SMUs in virtual spaces. To enhance immersion, SMUs incline to opt for 3D avatars for social interactions. However, existing 3D avatars are typically generated through scanning the real faces of SMUs, which can raise concerns regarding information privacy and security, such as profile identity leakages. To tackle this, we introduce a new framework for personalized 3D avatar construction, leveraging a two-layer network model that provides SMUs with the option to customize their personal avatars for privacy preservation. Specifically, our approach introduces avatar pseudonyms to jointly safeguard the profile and digital identity privacy of the generated avatars. Then, we design a novel metric named Privacy of Personalized Avatars (PoPA), to evaluate effectiveness of the avatar pseudonyms. To optimize pseudonym resource, we model the pseudonym distribution process as a Stackelberg game and employ Deep Reinforcement Learning (DRL) to learn equilibrium strategies under incomplete information. Simulation results validate the efficacy and feasibility of our proposed schemes for mobile social metaverses.

cs.NI↗