5 papers
Faltings' Isogeny Theorem via Equidistribution
Junyi Xie, Ziquan Yang
We give a new proof of Faltings' isogeny theorem. More precisely, we show that Yuan's non-archimedean equidistribution theorem can be used to "pump" homomorphisms and semisimplicit…
Picard rank jumps for families of K3 surfaces in positive characteristic
Ruofan Jiang, Ananth N. Shankar, Ziquan Yang
Let X/C be a non iso-trivial family of K3 surfaces over a curve C defined over characteristic p > 2 field. We show that if X avoids a necessary and structural obstruction coming fr…
The Tate conjecture for surfaces of geometric genus one -- embracing singularities
Haoyang Guo, Ziquan Yang
In this article, we aim to largely complete the program of proving the Tate conjecture for surfaces of geometric genus one, by introducing techniques to analyze those surfaces whos…
Pointwise criteria of p-adic local systems
Haoyang Guo, Ziquan Yang
Given a Z_p-linear local system over a smooth rigid space, we show that it is crystalline (resp. semi-stable) with respect to any smooth (resp. semi-stable) integral model if and o…
Arithmetic Deformation of Line Bundles
David Urbanik, Ziquan Yang
We introduce a new method to study mixed characteristic deformation of line bundles. In particular, for sufficiently large smooth projective families $f : \mathscr{X} \to \mathscr{…