Publications

  1. a-Numbers in Artin-Schreier covers (with Jeremy Booher)
    Algebra & Number Theory, to appear. arxiv, Magma code

  2. Breuil-Kisin modules via crystalline cohomology (with Tong Liu)
    Trans. Amer. Math. Soc., 371 (2019), no. 2, 1199--1230. arxiv, Erratum to published version

  3. The geometry of Hida families II: Λ-adic (φ,Γ)-modules and Λ-adic Hodge theory
    Compos. Math., 154 (2018), no. 4, 719--760. arxiv

  4. The Geometry of Hida families I: Λ-adic de Rham cohomology
    Math. Ann., 372 (2018), no. 1-2, 781--844. arxiv

  5. Dieudonné crystals and Wach modules for p-divisible groups (with Eike Lau)
    Proc. Lond. Math. Soc. (3), 114 (2017), no. 4, 733--763. arxiv

  6. On F-crystalline representations (with Tong Liu)
    Documenta Mathematica, 21 (2016), 223--270. arxiv

  7. A characterization of strictly APF extensions (with Chris Davis and Jonathan Lubin)
    J. Théorie Nombres Bordeaux, 28 (2016), no. 2, 417--430. arxiv

  8. Canonical Cohen rings for norm fields (with Chris Davis)
    Int. Math. Res. Not. IMRN (2015), no. 14, 5473--5517. arxiv

  9. On the Up-operator in characteristic p
    Math Res. Lett. 21 (2014), No. 2, pp. 1-6. arxiv

  10. Random Dieudonné Modules, Random p-Divisible Groups, and Random Curves Over Finite Fields (with Jordan Ellenberg and David Zureick-Brown)
    J. Inst. Math. Jussieu 12 (2013), No. 3, pp. 651-676. arxiv

  11. Canonical Extensions of Néron Models of Jacobians
    Algebra & Number Theory 4 (2010), No. 2, pp. 111-150. arxiv

  12. Canonical Integral Structures on the de Rham Cohomology of Curves
    Annales de l'Institut Fourier 59 (2009), No. 6, pp. 2255-2300. arxiv

  13. Modular Curves and Ramanujan's Continued Fraction (with Brian Conrad)
    J. Reine Angew. Math. (Crelle's Journal) 597 (2006), pp. 27-104. pdf, Erratum to Appendix D.

    Books Edited

  14. Perfectoid Spaces: Lectures from the 2017 Arizona Winter School
    Mathematical Surveys and Monographs 242, American Mathematical Society, Providence, RI., 2019, 297 pp. AMS Bookstore

    Ph.D. Thesis

  15. Compatibilities, correspondences, and integral structures in p-adic cohomology.
    The University of Michigan, 2007, supervised by Brian Conrad. pdf

See here for other expository notes and other mathematical writings.


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