10 papers
S-integrality for families of ordinary K3 surfaces and algebraicity theorems
Ruofan Jiang, Ananth N. Shankar
We prove an -integrality theorem for special divisors on GSpin Shimura varieties in positive characteristic. Let be a generically ordinary curve in such a Shimura variety no…
Quot scheme of points on torus knot singularities
Yifeng Huang, Ruofan Jiang, Alexei Oblomkov
For , we show that the moduli space of -codimensional -submodules of is paved by affine cells, by proving that each Białyni…
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…
-adic monodromy and mod unlikely intersections, II
Ruofan Jiang
We study ordinary abelian schemes in characteristic and their moduli spaces from the perspective of char Mumford--Tate, log Ax--Lindemann, and geometric André--Oort conject…
Matrix Points on Varieties
Asvin G, Yifeng Huang, Ruofan Jiang +1
We study the cohomology of , the moduli space of commuting -by- matrices satisfying the equations defining a quasi-projective scheme . This space can be viewed as…
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…
-adic monodromy and mod unlikely intersections, I
Ruofan Jiang
We formulate characteristic analogues of the Mumford--Tate and the André--Oort conjectures for ordinary mod Shimura varieties of Hodge type, and set up general frameworks f…
Punctual Quot schemes and Cohen--Lenstra series of the cusp singularity
Yifeng Huang, Ruofan Jiang
The Quot scheme of points on a variety over a field parametrizes quotient sheaves of of zero-dimensional support and len…
Splitting of almost ordinary abelian surfaces in families and the -integrality conjectures
Ruofan Jiang
Let be a non-isotrivial almost ordinary abelian surface with possibly bad reductions over a global function field of odd characteristic . Suppose is an infinite set of p…
Lattices in 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 . We identity both normal form…