This led Alexander Grothendieck to his conjectural theory of motives and motivated a search for an extension of Hodge theory, which culminated in the work of Pierre Deligne. He introduced the notion of a mixed Hodge structure, developed techniques for working with them, gave their construction (based on Heisuke Hironaka's resolution of singularities) and related them to the weights on l-adic cohomology, proving the last part of the Weil conjectures.
Alexander Grothendieck formulated his theory of motives and initiated efforts to extend Hodge theory. Pierre Deligne later realized this goal by introducing mixed Hodge structures, developing methods for working with them, providing their construction (based on Heisuke Hironaka's resolution of singularities), relating them to the weights in l-adic cohomology, and proving a part of the Weil conjectures.