arXiv subjects

Luciena Xiao Xiao

Publications and source records attributed to Luciena Xiao Xiao.

3 recordsLinked to original sources

arXiv2025

Monodromy and Irreducibility of Igusa Varieties

We determine the irreducible components of Igusa varieties for Shimura varieties of Hodge type under a mild condition and use that to compute the irreducible components of central leaves. In particular, we show that a strong version of the discrete Hecke orbit conjecture is false in general. Our method combines recent work of D'Addezio on monodromy groups of compatible local systems with a generalisation of a method of Hida, using the Honda--Tate theory for Shimura varieties of Hodge type developed by Kisin--Madapusi--Shin. We also determine the irreducible components of Newton strata in Shimura varieties of Hodge type by combining our methods with recent work of Zhou--Zhu.

math.NT↗

arXiv2022

Geometric quadratic Chabauty over number fields

This article generalizes the geometric quadratic Chabauty method, initiated over $\mathbb{Q}$ by Edixhoven and Lido, to curves defined over arbitrary number fields. The main result is a conditional bound on the number of rational points on curves that satisfy an additional Chabauty type condition on the Mordell-Weil rank of the Jacobian. The method gives a more direct approach to the generalization by Dogra of the quadratic Chabauty method to arbitrary number fields.

math.NT↗

arXiv2020

On The Hecke Orbit Conjecture for PEL Type Shimura Varieties

The Hecke orbit conjecture asserts that every prime-to-$p$ Hecke orbit in a Shimura variety is dense in the central leaf containing it. In this paper, we prove the conjecture for certain irreducible components of Newton strata in Shimura varieties of PEL type A and C, when $p$ is an unramified prime of good reduction. Our approach generalizes Chai and Oort's method for Siegel modular varieties.

math.NT↗