Ruofan Jiang

activity

20222026

collaborators

10 papers

math.NT2026

S-integrality for families of ordinary K3 surfaces and algebraicity theorems

Ruofan Jiang, Ananth N. Shankar

We prove an $S$ -integrality theorem for special divisors on GSpin Shimura varieties in positive characteristic. Let $C$ be a generically ordinary curve in such a Shimura variety no…

math.AG2026

Quot scheme of points on torus knot singularities

Yifeng Huang, Ruofan Jiang, Alexei Oblomkov

For $g cd (a, b) = 1$ , we show that the moduli space of $m$ -codimensional $k [[T^{a}, T^{b}]]$ -submodules of $k [[T]]^{n}$ is paved by affine cells, by proving that each Białyni…

math.AG2026

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…

math.NT2025

$p$ -adic monodromy and mod $p$ unlikely intersections, II

Ruofan Jiang

We study ordinary abelian schemes in characteristic $p$ and their moduli spaces from the perspective of char $p$ Mumford--Tate, log Ax--Lindemann, and geometric André--Oort conject…

math.AG2025

Matrix Points on Varieties

Asvin G, Yifeng Huang, Ruofan Jiang +1

We study the cohomology of $C_{n} (X)$ , the moduli space of commuting $n$ -by- $n$ matrices satisfying the equations defining a quasi-projective scheme $X$ . This space can be viewed as…

math.AG2023

Motivic Coh and Quot zeta functions of singular curves

Yifeng Huang, Ruofan Jiang

We present a general and effective algebraic framework for enumerating finite-length quotients of a torsion-free sheaf of arbitrary rank (the Quot zeta function) and finite-length…

math.NT2023

$p$ -adic monodromy and mod $p$ unlikely intersections, I

Ruofan Jiang

We formulate characteristic $p$ analogues of the Mumford--Tate and the André--Oort conjectures for ordinary mod $p$ Shimura varieties of Hodge type, and set up general frameworks f…

math.AG2023

Punctual Quot schemes and Cohen--Lenstra series of the cusp singularity

Yifeng Huang, Ruofan Jiang

The Quot scheme of points $Quot_{d, n} (X)$ on a variety $X$ over a field $k$ parametrizes quotient sheaves of $O_{X}^{\oplus d}$ of zero-dimensional support and len…

math.NT2023

Splitting of almost ordinary abelian surfaces in families and the $S$ -integrality conjectures

Ruofan Jiang

Let $A$ be a non-isotrivial almost ordinary abelian surface with possibly bad reductions over a global function field of odd characteristic $p$ . Suppose $Δ$ is an infinite set of p…

math.CO2022

Lattices in $F_{q} [[T]]^{d}$ and spiral shifting operators

Yifeng Huang, Ruofan Jiang

We investigate the algebra and combinatorics of an analogue of the Hermite normal form that classifies finite-index submodules of $F_{q} [[T]]^{d}$ . We identity both normal form…

S-integrality for families of ordinary K3 surfaces and algebraicity theorems

Quot scheme of points on torus knot singularities

Picard rank jumps for families of K3 surfaces in positive characteristic

p-adic monodromy and mod p unlikely intersections, II

Matrix Points on Varieties

Motivic Coh and Quot zeta functions of singular curves

p-adic monodromy and mod p unlikely intersections, I

Punctual Quot schemes and Cohen--Lenstra series of the cusp singularity

Splitting of almost ordinary abelian surfaces in families and the S-integrality conjectures

Lattices in Fq​[[T]]d and spiral shifting operators

$p$ -adic monodromy and mod $p$ unlikely intersections, II

$p$ -adic monodromy and mod $p$ unlikely intersections, I

Splitting of almost ordinary abelian surfaces in families and the $S$ -integrality conjectures

Lattices in $F_{q} [[T]]^{d}$ and spiral shifting operators