New refined obstructions control the Hasse principle and weak approximation for 0-cycles on generalised Kummer varieties and bielliptic surfaces assuming finiteness of Tate-Shafarevich groups, and address questions on Brauer-Manin versus connected descent.
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A new fibration theorem implies solvable descent, solving the Grunwald problem for solvable groups up to the Brauer-Manin obstruction.
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Solvable Descent and the Grunwald Problem for Solvable Groups
A new fibration theorem implies solvable descent, solving the Grunwald problem for solvable groups up to the Brauer-Manin obstruction.