Xinyao Zhang

collaborators

Showing math.NTShow all

3 papers · 1 filter

math.NT2026

Modular points and dimensions of Eisenstein deformation spaces

Xinyao Zhang

In this article, we study two-dimensional Eisenstein deformation spaces, focusing on the Zariski density of modular points and the dimensions of their irreducible components. Over…

math.NT2024

On the Fontaine-Mazur conjecture for $p = 3$

Xinyao Zhang

We prove the remaining $p = 3$ cases of the regular two-dimensional Fontaine-Mazur conjecture over $Q$ , thereby completing the regular case for all odd primes. Our main new…

math.NT2024

On the pro-modularity in the residually reducible case for some totally real fields

Xinyao Zhang

Let $p$ be an odd prime and $F$ an abelian totally real field of even degree in which $p$ splits completely. We study the fixed-determinant pseudo-deformation ring of $\mathbf{1}+\…

Modular points and dimensions of Eisenstein deformation spaces

On the Fontaine-Mazur conjecture for p=3

On the pro-modularity in the residually reducible case for some totally real fields

On the Fontaine-Mazur conjecture for $p = 3$