I am a faculty member of MCM, CAS and Institute of Mathematics, AMSS, CAS.
Address: Morningside Center of Mathematics, Zhongguancun Donglu 55 Hao, Beijing 100190, China
Email: wzheng@math.ac.cn

My research interest lies in algebraic geometry.
I defended my doctoral thesis at l'Université Paris-Sud in 2007 under the supervision of Luc Illusie.
I was a Ritt Assistant Professor at Columbia University. Here is my CV.

Séminaire de Géométrie Arithmétique Paris-Pékin-Tokyo (2012–present)

Conference on Arithmetic Geometry in honor of Luc Illusie (December 14–18, 2020)

My preprints on arXiv
My ORCID: http://orcid.org/0000-0002-6251-8468
My profile on MathSciNet (subscription required)

Kai-Wen Lan's links


Preprints

    (with Qing Lu) Categorical traces and a relative Lefschetz-Verdier formula, arXiv:2005.08522
    (with Qing Lu) ℓ-independence over Henselian valuation fields, appendix to Hiroki Kato, ℓ-independence of the trace of local monodromy in a relative case, arXiv:1904.02324
    (with Yifeng Liu) Enhanced adic formalism and perverse t-structures for higher Artin stacks, arXiv:1404.1128
    (with Yifeng Liu) Enhanced six operations and base change theorem for Artin stacks, arXiv:1211.5948
    (with Yifeng Liu) Gluing restricted nerves of ∞-categories, arXiv:1211.5294

Publications

Disclaimer: The arXiv identifiers are provided for convenience only. The published version may differ from the arXiv versions.

    (with Qing Lu) Compatible systems and ramification.
    Compos. Math. 155 (2019), no. 12, pp. 2334–2353. arXiv:1801.03221
    link
    (with Qing Lu) Duality and nearby cycles over general bases.
    Duke. Math. J. 168 (2019), no. 16, pp. 3135–3213. arXiv:1712.10216
    link
    Companions on Artin stacks.
    Math. Z. 292 (2019), no. 1–2, pp. 57–81. arXiv:1512.08929
    link
    (with Qing Lu and Zhiyong Zheng) On the distribution of Jacobi sums.
    J. Reine Angew. Math. 2018, no. 741, pp. 67–86. arXiv:1305.3405
    link
    Künneth formula for nearby cycles, appendix to Luc Illusie, Around the Thom–Sebastiani theorem.
    Manuscripta Math. 152 (2017), no. 1–2, pp. 119–123. arXiv:1604.07004
    link
    Gluing pseudo functors via n-fold categories.
    J. Homotopy Relat. Struct. 12 (2017), no. 1, pp. 189–271. arXiv:1211.1877
    link
    (with Shenghao Sun) Parity and symmetry in intersection and ordinary cohomology.
    Algebra Number Theory 10 (2016), no. 2, pp. 235–307. arXiv:1402.1292
    link note
    (with Luc Illusie) Quotient stacks and equivariant étale cohomology algebras: Quillen's theory revisited.
    J. Algebraic Geom. 25 (2016), no. 2, pp. 289–400. arXiv:1305.0365
    link corrigendum
    Six operations and Lefschetz-Verdier formula for Deligne-Mumford stacks.
    Sci. China Math. 58 (2015), no. 3 (special issue for Algebraic Geometry in East Asia 2013), pp. 565–632. arXiv:1006.3810
    link note
    On hyper base change.
    Exposé XII B in Travaux de Gabber sur l'uniformisation locale et la cohomologie étale des schémas quasi-excellents. Séminaire à l'École polytechnique 2006–2008, dirigé par Luc Illusie, Fabrice Orgogozo, Yves Laszlo.
    Astérisque 363–364 (2014), pp. 251–260.
    (with Luc Illusie) Odds and ends on finite group actions and traces.
    Int. Math. Res. Not. IMRN 2013, no. 1, pp. 1–62. arXiv:1001.1982
    link doi
    Errata and Addenda, Int. Math. Res. Not. IMRN 2014, no. 9, pp. 2572–2576. link doi
    Sur l'indépendance de l en cohomologie l-adique sur les corps locaux.
    Ann. Sci. Éc. Norm. Supér. (4) 42 (2009), no. 2, pp. 291–334. arXiv:0711.3658
    link
    Sur la cohomologie des faisceaux l-adiques entiers sur les corps locaux.
    Bull. Soc. Math. France 136 (2008), no. 3, pp. 465–503. arXiv:math/0701311
    link erratum
    (with Jin Yang) On a theorem of Chowla.
    J. Number Theory 106 (2004), no. 1, pp. 50–55.
    link note

Graduate theses

    Intégralité, rationalité et indépendance de l en cohomologie l-adique sur les corps locaux, thèse de doctorat effectuée à l'Université Paris-Sud, sous la direction de Luc Illusie, soutenue le 14 décembre 2007.
    Théorème de Gabber d'indépendance de l, mémoire de Master 2, dirigé par Luc Illusie, soutenu le 1er juillet 2005.

Slides

    Compatible systems along the boundary (Conference in honor of Ofer Gabber, 2018)
    Nearby cycles over general bases (Hong Kong Geometry Colloquium, 2017)
    代数叠、平展上同调、基变换（2012年）
    Weil猜想简介2（2011年清华）
    Mod l cohomology algebras of quotient stacks (PANT 2011, Beijing)
    Odds and ends on equivariant cohomology and traces (ICCM 2010, Beijing)


Past Events

    International Conference on Arithmetic Geometry in honor of Professor Michael Rapoport's 71st Birthday (March 18–22, 2019)
    Conference on Arithmetic Algebraic Geometry in honor of Professor Nicholas Katz's 71st Birthday (May 11–15, 2015)
    Summer Workshop on Arithmetic Geometry (July 22–25, 2013, with Shenghao Sun and Yichao Tian)
    Workshop on Perfectoid Spaces (August 6–10, 2012, with Yichao Tian)
    Workshop on Faltings' theory of almost étale extensions (August 3–14, 2009, with Yichao Tian)

Teaching

    Algebra I (Fall 2019, notes)
    Algebra III (commutative algebra, Spring 2019, summary)
    Algebra II (homological algebra, Spring 2015–2018, notes)
    Algebraic Number Theory 2 (Fall 2014, Fall 2016, Tsinghua, notes)
    Geometry of modular curves and arithmetic applications (Summer 2012, Tsinghua, with Yichao Tian)
    Basic Algebraic Geometry (Summer 2011, Tsinghua, with Xinwen Zhu)
    Abelian Varieties (Summer 2010, Tsinghua, with Yichao Tian, incomplete notes)
    Teaching at Columbia (2008–2012)

Notes

    Homological and homotopical algebra, notes for a talk in a reading seminar
    Laurent Lafforgue's Hua Loo-Keng Distinguished Lecture "What is the Langlands program all about?" (November 13, 2013)