Lei Zhang's Home Page

Lei Zhang
Room 237A, Lady Shaw Building
Department of Mathematics
The Chinese University of Hong Kong (CUHK)
Hong Kong, SAR China

Office: Room 237A, Lady Shaw Building - Map of Campus Map
Email: lzhang@math.cuhk.edu.hk
Phone: +852-3943-5139

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.algebra.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.
   
   

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. The arithmetic local Nori fundamental group (with M. Romagny and F. Tonini).
   https://arxiv.org/pdf/1711.06898.pdf.
   Submitted.
   
   
3. 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.
   Submitted.
   
   
4. 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.
   Submitted.
   
   
5. 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. An Introduction to \(\text{Bun}_G\). (Forschungsseminar at FU-Berlin, June 1, 2017)
   The latest version is here.
   
   

Last Modified: