arXiv subjects

Ningyi Li

Publications and source records attributed to Ningyi Li.

5 recordsLinked to original sources

arXiv2026

The Tate conjecture for abelian fivefolds over finite fields

We prove the Tate conjecture for abelian fivefolds over finite fields. The proof constructs correspondences for a residual motive using a Moret--Bailly family, Gross--Schoen heights, and monodromy. We also prove standard conjecture~$D_\ell$ over $\overline{\mathbf F}_p$ and independence of $\ell$ of rational cycle class kernels over algebraically closed fields of characteristic $p$. Over finite fields, rational and numerical equivalence agree with rational coefficients, and higher algebraic $K$-groups vanish rationally.

math.NT↗

arXiv2026

Exponents of factorized groups and Kashina's conjecture for group-theoretical Hopf algebras

Let $G=F\Gamma$ be a factorization of a finite group, with neither factor assumed normal and with $F\cap\Gamma$ allowed to be nontrivial. We prove that $\exp(G)$ divides $\operatorname{lcm}(|F|,|\Gamma|)$, or equivalently that $\gcd([G:F],[G:\Gamma])\exp(G)$ divides $|G|$. This answers a cohomological divisibility question posed by Natale. Combining the group-theoretic divisibility with Natale's exponent bound and a lifting argument, we prove Kashina's exponent conjecture, in the arbitrary-field formulation of Etingof and Gelaki, for every finite-dimensional semisimple and cosemisimple Hopf algebra $H$ over a field $k$ for which $\operatorname{Rep}(H\otimes_k\overline{k})$ is group-theoretical. The same argument proves the corresponding degree-three cohomological divisibility for coefficients in an arbitrary $G$-module. For complex group-theoretical categories, we also establish Frobenius-Schur exponent divisibility under a cohomological factorization hypothesis, without assuming a fiber functor. We derive applications to low-dimensional Hopf algebras and abelian extensions.

math.QA↗

arXiv2023

Self-assembly of Colloids with Competing Interactions Confined in Spheres

At low temperatures, colloidal particles with short-range attractive and long-range repulsive interactions can form various periodic microphases in bulk.In this paper, we investigate the self-assembly behaviour of colloids with competing interactions under spherical confinement by conducting molecular dynamics simulations. We find that the cluster, mixture, cylindrical, perforated lamellar and lamellar structures can be obtained, but the details of the ordered structures are different from those in bulk systems. Interestingly, the system tends to form more perforated structures when confined in smaller spheres. The mechanism behind this phenomenon is the relationship between the energy of the ordered structures and the bending of the confinement wall, which is different from the mechanism in copolymer systems.

cond-mat.soft↗

arXiv2023

Effects of Daily Exercise Time on the Academic Performance of Students: An Empirical Analysis Based on CEPS Data

This paper examines the effects of daily exercise time on the academic performance of junior high school students in China, with an attempt to figure out the most appropriate daily exercise time for students from the perspective of improving students' test scores. By dividing the daily exercise time into five sections to construct a categorical variable in a linear regression model as well as using another model to draw intuitive figures, I find that spending both too little and too much time on physical activity every day would have adverse impacts on students' academic performance, with differences existing in the impacts by gender, grade, city scale, and location type of the school. The findings of this paper carry implications for research, school health and education policy and physical and general education practice. The results also provide recommendations for students, parents and teachers.

econ.GN↗

arXiv2023

Forecasting and Analysis of CSI 300 Daily Index and S&P 500 Index Based on ARMA and GARCH Models

In this paper, the ARMA(0,6)-GARCH(1,1) and ARMA(2,6)-eGARCH(1,1) models are constructed by applying ARMA and GARCH models to daily data of the CSI 300 and S&P 500 indices from 2018 to 2021, and the forecasts for the next 7 steps and the corresponding VaR and ES are calculated. After testing the sensitivity of the models, the two index stocks are compared and the corresponding conclusions are presented.

stat.AP↗