Strong approximation: Arithmetic purity and squarefree value
Date
Thursday, November 14, 2019 13:30 - 15:30
Speaker
Yang CAO (University of Hannover)
Location
Heinzel Seminar Room / Office Bldg West (I21.EG.101)
Series
Seminar/Talk
Tags
Mathematics and CS Seminar
Host
Timothy Browning
Contact
Strong approximation with Brauer-Manin obstruction is defined by Colliot-Thelene and Xu to study the local-global principle for the integral points. For an algebraic variety, inspired by analytic number theory, I consider the density of integral points with coprime values or squarefree values in adelic space: the arithmetic purity or squarefree values of strong approximation. On the other side, for a semi-simple, simply connected k-simple linear algebraic group G, it is conjectured by Wittenberg that G satisfies arithmetic purity: the complement of any codimension >=2 closed subset satisfies strong approximation. We prove this conjecture for k-isotropic groups by an analogue of fibration method and for Spin groups by using the density of rational points with almost prime polynomial values. This is joint work with Zhizhong Huang.