4 papers
math.NT2026
Strengthenings of Mazur's Conjecture for Higher Heegner Points
Xiaoyu Zhang
We establish quantitative strengthenings of Mazur's conjecture regarding the non-torsion property of higher Heegner points on modular and Shimura curves, confirming both a vertical…
math.NT2025
Automorphic side of Taylor-Wiles method for orthogonal and symplectic groups
Xiaoyu Zhang
The core of the Taylor-Wiles and Taylor-Wiles-Kisin method in proving modularity lifting theorems is the construction of Taylor-Wiles primes satisfying certain conditions relating…
math.NT2025
Non-vanishing mod of theta lifts for (O_{2n+1},Mp_{4n})
Xiaoyu Zhang
We establish the non-vanishing mod of certain global theta lifts from a compact orthogonal group over to a metaplectic group …
math.NT2025
Simultaneous supersingular reductions of abelian varieties
Xiaoyu Zhang
For a point in a Shimura variety attached to a Shimura datum of Hodge type , we have an associated abelian scheme . Fixing a non-empty finite set of…