I am interested in arithmetic geometry, in particular, in various forms of p-adic geometry. My primary research area is p-adic Hodge theory, namely Breuil-Kisin modules, prismatic cohomology and their applications. I am also interested in modular and automorphic froms, rational points on higher genus curves, homological algebra and its interaction with algebraic geometry.
| [5] | Ramification bounds via Wach modules and q-crystalline cohomology | [pdf] |
| Preprint. | ||
| [4] | Constructing vector-valued automorphic forms on unitary groups | [arXiv] |
| with T. Browning, E. Eischen, C. Frechette, S. Hong, S. Y. Lee, D. Marcil; preprint. | ||
| [3] | Crystalline condition for Ainf-cohomology and ramification bounds | [arXiv] |
| preprint based on my PhD thesis, submitted. | ||
| [2] | Geometric quadratic Chabauty over number fields | [arXiv] |
| with D. Lilienfeldt, L. Xiao, Z. Yao; Trans. Amer. Math. Soc. 376 (2023), 2573-2613 | [Journal] | |
| [1] | Cotilting sheaves on Noetherian schemes | [arXiv] |
| with J. Šťovíček; Math. Z. 296, 275–312 (2020) | [Journal] |
Introduction to Shimura varieties. [link] These are notes taken during Elena Mantovan's minicourse on Shimura varieties during the Pair of Automorphic Workshops at the University of Oregon in July 2022. (No originality claimed.)
Čech complexes for crystalline cohomology. [pdf] This note is a long-ish proof of the (also quite long) unproved Remark 07MM of the Stacks Project, about a variant of Čech complex that computes crystalline cohomology.
An example of ln-formally étale map that is not weakly étale. [pdf] This example came about as a part of a project that I participated in during the Arizona Winter School in March 2019. The project was associated with M. Morrow's lecture series "Topological Hochschild homology in arithmetic geometry". The project assistant was B. Antieau.
\pi-typical Witt vectors. [pdf] This note is a write-up of some basic properties of the (p-typical) Witt vectors construction adjusted to a uniformizer \pi of a local number field, with tediously elementary proofs. (No originality claimed.)