A mod p variant of the Andr\'e-Oort conjecture

TL;DR

This paper proves a variant of the Andre9-Oort conjecture for the product of two modular curves in positive characteristic, under the assumption of GRH for quadratic fields, advancing understanding in arithmetic geometry.

Contribution

It introduces and proves a new variant of the Andre9-Oort conjecture specifically for modular curves in positive characteristic, assuming GRH.

Findings

Proves a mod p version of the Andre9-Oort conjecture for two modular curves.

Establishes results conditional on GRH for quadratic fields.

Contributes to the understanding of special points in positive characteristic settings.

Abstract

We state and prove a variant of the Andr\'e-Oort conjecture for the product of 2 modular curves in positive characteristic, assuming GRH for quadratic fields.