Lei Zhang's Home Page

Lei Zhang
Room A444, Hai Qin 2
School of Mathematics (Zhuhai)
Sun Yat-Sen University (SYSU)
Zhuhai, Guangdong Province
People's Republic of China

Office: Room A444, Hai Qin 2- Map of Campus Map
Email: zhanglei85@mail.sysu.edu.cn

Here is my CV
Here is my PhD thesis

Publications

1. The Homotopy Sequence for Nori's Fundamental Group
   Journal of Algebra, Vol. 393, pp. 79 - 91, doi: https://doi.org/10.1016/j.jalgebra.2013.07.010, 2013.
   
   
2. The Homotopy Sequence for the Algebraic Fundamental Group
   International Mathematics Research Notices, no. 22, 6155-6174., doi: 10.1093/imrn/rnt163, 2014.
   
   
3. Nori's Fundamental Group over a non Algebraically Closed Field
   Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Vol. XVIII, pp. 1349-1394, doi: 10.2422/2036-2145.201604_007, 2018.
   
   
4. Algebraic and Nori Fundamental Gerbes (with Fabio Tonini)
   Journal of the Institute of Mathematics of Jussieu, no. 4, 855-897. doi: 10.1017/S147474801700024X, 2019.
   
   
5. F -divided sheaves trivialized by dominant maps are essentially finite (with Fabio Tonini)
   Transactions of the American Mathematical Society, Volume 371, Number 8, 15 April 2019, Pages 5529-5549, doi: https://doi.org/10.1090/tran/7444, 2019.
   
   
6. Nori fundamental gerbe of essentially finite covers and Galois closure of towers of torsors (with M. Antei, I. Biswas, M. Emsalem, F. Tonini)
   Selecta Mathematica, no. 2, Paper No. 18, 37 pp, doi: https://doi.org/10.1007/s00029-019-0449-z, 2019.
   
   
7. Essentially Finite Vector Bundles on Normal Pseudo-proper Algebraic Stacks (with Fabio Tonini)
   Documenta Mathematica, 25, 159-169, doi: 10.25537/dm.2020v25.159-169, 2020.
   
   
8. The arithmetic local Nori fundamental group (with M. Romagny and F. Tonini)
   Transactions of the American Mathematical Society, Volume 374, Number 12, Pages 8869–8885, doi: 10.1090/tran/8504, 2021.
   
   
9. A crystalline incarnation of Berthelot's conjecture and Künneth formula for isocrystals (with V. Di Proietto and F. Tonini)
   Journal of Algebraic Geometry, doi: https://doi.org/10.1090/jag/789
   
   
10. A generalized Abhyankar's conjecture for simple Lie algebras in characteristic \(p>5\) (with S. Otabe and F. Tonini)
    Mathematische Annalen, 383, 1–54, doi: https://doi.org/10.1007/s00208-021-02269-5, 2022.
    
    

Prepublications

1. A theorem on meromorphic descent and the specialization of the pro-étale fundamental group (with Marcin Lara, Jiu-Kang Yu)
   https://arxiv.org/abs/2103.11543.pdf
   Submitted.
   
   
2. Frobenius fixed objects of moduli (with V. Di Proietto and F. Tonini)
   https://arxiv.org/pdf/2012.14075.pdf
   Submitted.
   
   
3. A comparison theorem for the pro-étale fundamental group (with Jiu-Kang Yu)
   https://arxiv.org/pdf/2206.01383.pdf
   Submitted.
   
   

Teaching

2020-2021 Term2, I taught a course Linear Algebra I in CUHK.

Summer semester 2018 I hold a student seminar on Quadratische Formen.

Winter semester 2017-2018 I taught a course on Crystals and Crystalline Cohomology.

Students

I have supervised a master student Ragnarsson Amazeen, here is his thesis.

Some Lecture Notes

1. The Nori Local Fundamental Group (RECENT TRENDS IN ALGEBRA, GEOMETRY, AND ARITHMETIC, June 11, 2022)
   The latest version is here .
   
   
2. Fundamental Groups in Algebraic Geometry (CNU Summer School at Beijing, July 3, 2021)
   The latest version is here .
   
   
3. An Introduction to \(\text{Bun}_G\). (Forschungsseminar at FU-Berlin, June 1, 2017)
   The latest version is here.
   
   

Last Modified: 8. March 2023.