Year: 2026
Type: preprint
Abstract: 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 not contained in any special divisor. Then, for any increasing sequence of prime-to-$p$ positive integers $m_i$ and any finite set of closed points $S\subset C$, we prove that $C\setminus S$ meets the special divisor $Z(m_i)$ for all but finitely many $i$. The key new input is an algebraicity theorem for formal special endomorphisms which allows us to use techniques from Diophantine approximation. We prove this algebraicity theorem using a punctual monodromy theorem and a positive-characteristic analogue of the Mumford--Tate conjecture.
Source: arXiv (Cornell University)
Authors: Jiang, Ruofan, Shankar, Ananth N.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214128304