In mathematics, Jean-Pierre Serre conjectured[1][2] the following statement regarding the Galois cohomology of a simply connected semisimple algebraic group.
This is a special case of the Kneser–Harder–Chernousov Hasse principle for algebraic groups over global fields.
[2]) The conjecture also holds when F is finitely generated over the complex numbers and has transcendence degree at most 2.
[5] Building on this result, the conjecture holds if G is a classical group.
[6] The conjecture also holds if G is one of certain kinds of exceptional group.