Research
p-isogenies with G-structure
joint with Keerthi Madapusi
We construct stacks of p-isogenies with G-structure over Shimura varieties of abelian type at hyperspecial level.
(in preparation)
Unramifiedness of weight one representations for Hilbert modular varieties
In this paper, I show that if the residual degree is odd, then the mod p Galois representation attached to a Hecke eigenclass in the higher coherent cohomology of the Hilbert modular variety in weight one is unramified at p.
(Warning: This paper is currently still in draft form, and will be continually revised)
Constructing vector-valued automorphic forms on unitary groups
joint with Thomas L. Browning, Pavel Coupek, Ellen Eischen, Claire Frechette, Serin Hong and David Marcil
In this paper, we extend ideas of Clery-van der Geer in the Siegel case to construct autormphic forms on unitary Shimura varieties via differential operators.
Torsion vanishing for some Shimura varieties
joint with Linus Hamann
In this paper, we extend the results of Caraiani-Scholze and show torsion vanishing of l-adic étale cohomology of some PEL type Shimura varieties.
Semisimplicity of étale cohomology for some Shimura varieties
In this paper, I show that some part of the étale cohomology of some abelian type Shimura varieties is semisimple as a Galois representation.
Eichler-Shimura relations for Shimura varieties of Hodge type
In this paper, I show the Eichler-Shimura congruence relations for a large class of Shimura varieties of Hodge type, confirming a conjecture of Blasius-Rogawski. This is the main result of my PhD thesis.