Lei Zhang's Home Page

Lei Zhang
Room 410, Academic Building
Institute of Mathematical Science (IMS)
The Chinese University of Hong Kong (CUHK)
Hong Kong, SAR China

Office: Room 410, Academic Building - Map of Campus Map
Email: lzhang@ims.cuhk.edu.hk
Phone: +852-3943-3717

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.
   
   

Prepublications

1. A crystalline incarnation of Berthelot's conjecture and Künneth formula for isocrystals (with V. Di Proietto and F. Tonini).
   https://arxiv.org/pdf/1812.05153.pdf.
   To appear in Journal of Algebraic Geometry.
   
   
2. A generalized Abhyankar's conjecture for simple Lie algebras in characteristic \(p>5\) (with S. Otabe and F. Tonini).
   https://arxiv.org/pdf/2003.03240.pdf.
   To appear in Mathematische Annalen.
   
   
3. 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.
   
   
4. Frobenius fixed objects of moduli (with V. Di Proietto and F. Tonini).
   https://arxiv.org/pdf/2012.14075.pdf.
   Submitted.
   
   

Teaching

2020-2021 Term2, I am teaching 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. Fundamental Groups in Algebraic Geometry (CNU Summer School at Beijing, July 3, 2021)
   The latest version is here .
   
   
2. An Introduction to \(\text{Bun}_G\). (Forschungsseminar at FU-Berlin, June 1, 2017)
   The latest version is here.
   
   

Last Modified: Oktober 27, 2021.