Members

Shizhang Li(李时璋)

Email:lishizhang@amss.ac.cn

Office:MCM Building(晨兴楼) 506，Morningside Center of Mathematics, No.55, Zhongguancun East Road, Beijing, 100190, China

Research interest:

Arithmetic Geometry

I am currently an associate professor at the Morningside Center of Mathematics, Beijing, China. My research interest mainly rests in arithmetic geometry. Currently I am mainly working on p-adic Hodge theory and related problems in various p-adic cohomology theory and p-adic geometry. I am also interested in algebraic geometry with an infinity categorical flavor, finding/studying concrete interesting geometric examples. One particular such of my current focus is finite flat commutative group schemes and their classifying stacks.

Vitae
(Pre)publications
Teaching
中文版

Education:

2014/09-2019/06 Ph.D Columbia University, New York, US, Supervisors: Aise Johan de Jong

2010/09-2014/07 B.S Zhejiang University, Hangzhou, China

Employment:

2019/09-2022/06, Donald J. Lewis Research Assistant Professor, University of Mich-igan

2022/07-present, Associate Proefssor, Academy of Mathematics and Systems Science, CAS

Publications & Preprints:

1. Shizhang Li, On rigid varieties with projective reduction; J. Algebraic Geom. 29 (2020), 669-690.

2. Shizhang Li, Semistable reduction for multi-filtered vector spaces, arxiv: 1704.03968.

3. David Hansen, Shizhang Li, Line bundles on rigid varieties and Hodge symmetry, Math. Z. 296 (2020), 1777-1786.

4. Shizhang Li, Xuanyu Pan, Logarithmic de Rham comparison for open rigid spaces, Forum Math. Sigma J. Math. 7 (2019), e32.

5. Shizhang Li, An example of liftings with different Hodge numbers, Math. Res. Lett. 27 (2020), 835-844.

6. Shizhang Li, Xuanyu Pan, Unobstructedness of deformations of Calabi—Yau varieties with a line bundle, arxiv: 1310.7162.

7. Shizhang Li, Integral p-adic Hodge filtrations in low dimension and ramification, J. Eur. Math. Soc. (2022), published online first.

8. Brian Lawrence, Shizhang Li, A counterexample to an optimistic guess about étale local systems, C. R. Math. Acad. Sci. Paris. 359 (2021), 923-924.

9. Haoyang Guo, Shizhang Li, Period sheaves via derived de Rham cohomology, Compos. Math. 157 (2021), 2377-2406.

10. Shizhang Li, Tong Liu, Comparison of prismatic cohomology and derived de Rham cohomology, arxiv: 2012.14064.

11. Bhargav Bhatt, Shizhang Li, Totaro’s inequality for classifying spaces, arxiv: 2107.04111.

12. Shizhang Li, Shubhodip Mondal, On endomorphisms of the de Rham cohomology functor, Geom. Topol. to appear.

13. Shizhang Li, Dingxin Zhang, Exponentially twisted de Rham cohomology and rigid cohomology, arxiv: 2111.05689.

14. Shizhang Li, Tong Liu, On the u∞-torsion submodule of prismatic cohomology, arxiv: 2204.03411.

研究方向

p进几何

教育经历

2014年9⽉ — 2019年5⽉22⽇，哥伦⽐亚⼤学 (美国纽约) ，数学博⼠,

导师: Aise Johan de Jong

2010年9⽉ — 2014年6⽉，浙江⼤学 (中国杭州) ，数学学⼠,

工作经历

2022年6⽉⾄今中国科学院·数学与系统科学研究院·晨兴数学中⼼，副研究员

2023-2024学年访问⾼等研究院

2019年9⽉1⽇ — 2022年5⽉31⽇密西根⼤学，博⼠后

文章与预印本

18. Automorphisms of Frobenius twisted de Rham cohomology (with Shubhodip

Mondal), arXiv.

17. Bounding crystalline torsion from étale torsion (with Ofer Gabber), arXiv.

16. Relative Poincaré duality in nonarchimedean geometry (with Emanuel Reinecke

and Bogdan Zavyalov), arXiv.15. Frobenius height of prismatic cohomology with coefficients (with Haoyang Guo),

arXiv.

14. On the u∞-torsion submodule of prismatic cohomology (with Tong Liu), arXiv.

Compositio Mathematica, Volume 159, Issue 8, August 2023, pp. 1607-1672, doi: https://

doi.org/10.1112/S0010437X23007261.

13. Exponentially twisted de Rham cohomology and rigid cohomology (with Dingxin

Zhang), arXiv. Math. Ann. 390, 639–670 (2024), doi: https://doi.org/10.1007/

s00208-023-02772-x.

12. On endomorphisms of the de Rham cohomology functor (with Shubhodip

Mondal), arXiv. Geom. Topol. 28 (2024), no. 2, 759–802, doi: 10.2140/gt.2024.28.759.

11. Totaro’s inequality for classifying spaces (with Bhargav Bhatt), arXiv.

10. Comparison of prismatic cohomology and derived de Rham cohomology (with

Tong Liu), arXiv. J. Eur. Math. Soc. 27 (2025), no. 1, pp. 183–268, doi: 10.4171/JEMS/

1377.

9. Period sheaves via derived de Rham cohomology (with Haoyang Guo), arXiv.

Compositio Mathematica, Volume 157, Issue 11, November 2021, pp. 2377-2406, doi: https://

doi.org/10.1112/S0010437X21007545.

8. A counterexample to an optimistic guess about étale local systems (with Brian

Lawrence), arXiv. C. R. Math. Acad. Sci. Paris 359 (2021), 923-924, doi: 10.5802/

crmath.229.

7. Integral p-adic Hodge filtrations in low dimension and ramification, arXiv. J. Eur.

Math. Soc. 24 (2022), no. 11, pp. 3801–3827, doi: 10.4171/JEMS/1237.

6. Unobstructedness of deformations of Calabi—Yau varieties with a line bundle

(with Xuanyu Pan), arXiv.

5. An example of liftings with different Hodge numbers, arXiv, Mathematical Research

Letters, Vol. 27, No. 3 (2020), pp. 835-844, doi: https://dx.doi.org/10.4310/

MRL.2020.v27.n3.a10.

4. Logarithmic de Rham comparison for open rigid spaces (with Xuanyu Pan), arXiv,

Forum Math. Sigma, volume 7 (2019), e32, doi: 10.1017/fms.2019.27.

3. Line bundles on rigid varieties and Hodge symmetry (with David Hansen), arXiv,

Mathematische Zeitschrift 296, 1777-1786 (2020), doi: https://doi.org/10.1007/

s00209-020-02535-3.

2. Semistable reduction for multi-filtered vector spaces, arXiv.

1. On rigid varieties with projective reduction, arXiv, J. Algebraic Geom. 29 (2020),

669-690, doi: https://doi.org/10.1090/jag/740.