Hodge theory and the cohomology of complex varieties

Specialeforsvar ved Brandon Israel Garcia Flores

 Titel: Hodge theory and the cohomology of complex varieties

Abstract: A study and exposition of Mixed Hodge .eory as originally introduced by Pierre Deligne in his papers “Theorie de Hodge: II” and “Theorie de Hodge: III”, where mixed Hodge structures are defined. These structures allow us to drop the smoothness and completeness assumptions used in classical Hodge Theory when working with the cohomology groups of complex algebraic varieties, and adopt a more general setting. Moreover, the collection of mixed Hodge structures forms an abelian category, and it can be shown that cohomology, seen as as a collection of functors, can be lifted to this new category.

Vejleder: Søren Galatius
Censor:   Iver M Ottosen, AAU