Research Interest: I am interested in number theory and algebraic geometry. I mostly work in arithmetic algebraic geometry.
Some more specific themes in my research have been the integral models of Shimura varieties.
Research Interest: I am interested in number theory and algebraic geometry. I mostly work in arithmetic algebraic geometry.
Some more specific themes in my research have been the integral models of Shimura varieties.
Publications and pre-prints:
10. On semi-stable integral models for Shimura varieties, (with J. Yang and Z. Zhao), 2026, arXiv:2608.07105.
Abstract: We construct (potentially) semi-stable integral models for a class of Shimura varieties with maximal parahoric level at an odd prime p. The main input is an explicit construction of semi-stable equivariant modifications of the relevant canonical local models, where the underlying groups are Weil restrictions of unramified unitary similitude groups, symplectic similitude groups, or even orthogonal similitude groups. Via the local model diagram, these constructions give (potentially) semi-stable integral models of the corresponding Shimura varieties. In particular, the resulting models are regular and have reduced special fiber with normal crossings. As an application, we deduce the unipotence of the inertia action on nearby cycles and the l-adic cohomology of the geometric generic fibers.
9. On p-adic integral moduli schemes and local models for PEL type D, (with J. Yang and Z. Zhao), 2026, arXiv:2602.23813.
Abstract: We construct flat integral moduli schemes of PEL type D and the corresponding flat orthogonal Rapoport--Zink spaces with parahoric level structure over a p-adic integer ring. The construction relies on proving a conjecture of Pappas--Rapoport: for an even orthogonal similitude group over a complete discretely valued field of residue characteristic p>2, and for arbitrary parahoric level, the associated spin local model is flat, normal, Cohen--Macaulay, with reduced special fiber. In the course of the proof, we also show that in the quasi-split but non-split case, the Rapoport--Zink (naive) local model is topologically flat, verifying a conjecture of Pappas--Rapoport--Smithling. In the maximal parahoric case, we also describe the Schubert varieties in the special fiber in moduli-theoretic terms. Finally, for a maximal parahoric case we construct an explicit regular semi-stable model by blowing up the spin local model along the unique closed Schubert cell in its special fiber.
8. The basic locus of regular ramified unitary Rapoport-Zink spaces at vertex-stabilizer level, (with Z. Zhao), 2025, arXiv:2511.05576.
Abstract: We construct the Bruhat-Tits stratification of the reduced basic locus of regular ramified unitary Rapoport-Zink spaces of signature (n-1,1) at vertex-stabilizer level. To study the Bruhat-Tits strata, we introduce strata models--simpler models that are étale-locally isomorphic to each stratum. They admit two complementary characterizations: (i) as strict transforms under the blow-up of the local model at its worst point, and (ii) via a partial moduli description given by explicit linear-algebraic conditions; from these we deduce smoothness, explicit dimension formulas and irreducibility of the Bruhat-Tits strata.
7. The basic locus of unitary splitting Rapoport-Zink spaces with vertex stabilizer level, (with Z. Zhao), 2025, arXiv:2510.14497.
Abstract: We construct the Bruhat-Tits stratification of the ramified unitary splitting Rapoport-Zink space, with the level being the stabilizer of a vertex lattice. To determine certain local properties of the Bruhat-Tits strata, we develop a theory of the strata splitting models. To study their global structure, we establish an explicit isomorphism between the Bruhat-Tits strata and certain (modified) Deligne-Lusztig varieties.
6. On the geometry of splitting models, (with S. Bijakowski & Z. Zhao), 2025, arXiv:2501.05950.
Abstract: We consider Shimura varieties associated to a unitary group of signature (n−s,s) where n is even. For these varieties, by using the spin splitting models from Zachos-Zhao, we construct flat, Cohen-Macaulay, and normal p-adic integral models with reduced special fiber and with an explicit moduli-theoretic description over odd primes p which ramify in the imaginary quadratic field with level subgroup at p given by the stabilizer of a π-modular lattice in the hermitian space. We prove that the special fiber of the corresponding splitting model is stratified by an explicit poset with a combinatorial description, similar to Bijakowski-Hernandez, and we describe its irreducible components. Additionally, we prove the closure relations for this stratification.
5. Semi-stable and splitting models for unitary Shimura varieties over ramified places. II, (with Z. Zhao), International Mathematics Research Notices, Volume 2025, Issue 11, June 2025, https://doi.org/10.1093/imrn/rnaf145.
Abstract: We consider Shimura varieties associated to a unitary group of signature (n-1,1). For these varieties, we construct p-adic integral models over odd primes p which ramify in the imaginary quadratic field with level subgroup at p given by the stabilizer of a vertex lattice in the hermitian space. Our models are given by a variation of the construction of the splitting models of Pappas-Rapoport and they have a simple moduli theoretic description. By an explicit calculation, we show that these splitting models are normal, flat, Cohen-Macaulay and with reduced special fiber. In fact, they have relatively simple singularities: we show that a single blow-up along a smooth codimension one subvariety of the special fiber produces a semi-stable model. This also implies the existence of semi-stable models of the corresponding Shimura varieties.
4. Semi-stable and splitting models for unitary Shimura varieties over ramified places. I, (with Z. Zhao), Forum of Mathematics, Sigma 13 (2025): e119, https://doi.org/10.1017/fms.2025.10079.
Abstract: We consider Shimura varieties associated to a unitary group of signature (n-s,s) where n is even. For these varieties, we construct smooth p-adic integral models for s=1 and regular p-adic integral models for s=2 and s=3 over odd primes p which ramify in the imaginary quadratic field with level subgroup at p given by the stabilizer of a π-modular lattice in the hermitian space. Our construction, which has an explicit moduli-theoretic description, is given by an explicit resolution of a corresponding local model.
3. Semi-stable models for some unitary Shimura varieties over ramified primes, preprint (2024), Algebra & Number Theory, Vol. 18 (2024), No. 9, 1715–1736.
Abstract: We consider Shimura varieties associated to a unitary group of signature (n-2,2). We give regular p-adic integral models for these varieties over odd primes p which ramify in the imaginary quadratic field with level subgroup at p given by the stabilizer of a selfdual lattice in the hermitian space. Our construction is given by an explicit resolution of a corresponding local model.
2. Regular integral models for Shimura varieties of orthogonal type, (with G. Pappas), Compos. Math. 158(4) (2022), 831-867.
Abstract: We consider Shimura varieties for orthogonal or spin groups acting on hermitian symmetric domains of type IV. We give regular p-adic integral models for these varieties over odd primes p at which the level subgroup is the connected stabilizer of a vertex lattice in the orthogonal space. Our construction is obtained by combining results of Kisin and the first author with an explicit presentation and resolution of a corresponding local model.
1. On orthogonal local models of Hodge type, International Mathematics Research Notices, Volume 2023, Issue 13, (2023), 10799–10836.
Abstract: We study local models that describe the singularities of Shimura varieties of non-PEL type for orthogonal groups at primes where the level subgroup is given by the stabilizer of a single lattice. In particular, we use the Pappas-Zhu construction and we give explicit equations that describe an open subset around the ``worst" point of orthogonal local models given by a single lattice. These equations display the affine chart of the local model as a hypersurface in a determinantal scheme. Using this we prove that the special fiber of the local model is reduced and Cohen-Macaulay.
Ph.D Thesis: "On Orthogonal Local Models of Shimura Varieties". The results of my thesis have been superseded by those in the papers (5) & (6). If you would still like to see it, click here.
Co-organizer (with J. Lourenço and E. Viehmann) of the Oberseminar at the University of Münster on "Affine Deligne-Lusztig theory", Spring 2025.