King's conjecture on exceptional collections of line bundles

A smooth toric variety is a variety defined by a smooth complete fan, and an exceptional collection of line bundles is a sequence of line bundles forming an exceptional collection in its derived category; it is full if it generates the derived category and strong if all higher Ext groups between its objects vanish.

King's conjecture. Every smooth toric variety possesses a full strong exceptional collection of line bundles.

This conjecture concerns the existence of particularly well-behaved generators for derived categories of coherent sheaves on smooth toric varieties. The source attributes it to Alastair King; no resolution status is supplied here.