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.
This prompted Alexander Grothendieck to his conjectural theory of motives and inspired a quest for an extension of Hodge theory, which was realized in Pierre Deligne's work. He introduced the concept of a mixed Hodge structure, devised methods to handle them, outlined their construction (based on Heisuke Hironaka's resolution of singularities), linked them to the weights in l-adic cohomology, and confirmed the latter part of the Weil conjectures.