Colloquium abstracts

R. Parimala
Emory University, U.S.A.
May 16, 2019

Local-global principle for reductive groups over arithmetic surfaces:  There has been progress in the study of local-global principle for existence of rational points on principal homogeneous spaces under connected linear algebraic groups defined over function fields of curves over complete discrete valued fields, thanks to the patching techniques developed by Harbater-Hartmann-Krashen. An interesting case is when the group is defined over the complete discrete valuation ring. We discuss some recent progress in this study with special reference to tori.