3 papers
math.NT2026
Zariski density of modular points in the Eisenstein case
Xinyao Zhang
In this article, we study the Zariski closure of modular points in the two-dimensional universal deformation space when the residual Galois representation is reducible. Unlike the…
math.NT2025
On the Fontaine-Mazur conjecture for
Xinyao Zhang
In this article, we prove the remaining open cases of the Fontaine-Mazur conjecture on two-dimensional regular Galois representations over $\Gal(\overline{\Q}/\Q)$ when , henc…
math.NT2025
On the pro-modularity in the residually reducible case for some totally real fields
Xinyao Zhang
In this article, we study the relation between the universal deformation rings and big Hecke algebras in the residually reducible case. Following the strategy of Skinner-Wiles and…