Thematic Programme on Rational Points, Algebraic Cycles and the Local-Global Principle

Variants of the local-global principle beginning with Hasse's theorem for quadratic forms are many. Extension of Hasse's theorem to homogeneous spaces of connected linear algebraic groups over a number field, and to homogeneous spaces of linear algebraic groups over function fields in one variable over a local field are two such variants. Conjectures concerning the existence of rational points and zero-cycles, and their interactions with analytic number theory and motivic cohomology fall under the realm of this study. Involving objects like Brauer group and Chow groups, and drawing techniques from algebraic K-theory, this programme sets out to examine recent progress in these areas.