Hodge Ideals

Mircea Mustata, University of Michigan, Ann Arbor.Mihnea Popa, Northwestern University, Evanston, IL.

• IntroductionPreliminariesSaito's Hodge filtration and Hodge modulesBirational definition of Hodge idealsBasic properties of Hodge idealsLocal study of Hodge idealsVanishing theoremsVanishing on $\mathbf{P} ^n$ and abelian varieties, with applicationsAppendix: Higher direct images of forms with log polesReferences.