TalksArithmetic purity of strong approximation for linear algebraic groups
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Yang Cao ( Shandong University, China )
2025-08-19 10:30-11:30 & 14:10-15:10
Room 440, Astronomy and Mathematics Building
Strong approximation is a fundamental method for studying the local-global principle for integral solutions of Diophantine equations. Inspired by topological purity theory, we investigate the arithmetic purity of strong approximation, which is to study the integral solutions of Diophantine equations under an additional coprimality condition (requiring values to be coprime with respect to two fixed polynomials).
In the first part, I will present a survey on strong approximation with the Brauer-Manin obstruction and its generalizations (including arithmetic purity) for linear algebraic groups and homogeneous spaces.
In the second part, I will focus on my joint work with Zhizhong Huang and Runlin Zhang, where we establish the arithmetic purity of strong approximation for isotropic linear algebraic groups and spin groups. Our proof combines analytic methods (such as the density of points with almost prime polynomial values) and arithmetic techniques.