On Saito’s Vanishing Theorem
نویسنده
چکیده
We reprove Saito’s vanishing theorem for mixed Hodge modules by the method of Esnault and Viehweg. The main idea is to exploit the strictness of direct images on certain branched coverings.
منابع مشابه
Kodaira-saito Vanishing and Applications
The first part of the paper contains a detailed proof of M. Saito’s generalization of the Kodaira vanishing theorem, following the original argument and with ample background. The second part contains some recent applications, and a Kawamata-Viehweg-type statement in the setting of mixed Hodge modules.
متن کاملVanishing of Ext-Functors and Faltings’ Annihilator Theorem for relative Cohen-Macaulay modules
et be a commutative Noetherian ring, and two ideals of and a finite -module. In this paper, we have studied the vanishing and relative Cohen-Macaulyness of the functor for relative Cohen-Macauly filtered modules with respect to the ideal (RCMF). We have shown that the for relative Cohen-Macaulay modules holds for any relative Cohen-Macauly module with respect to with ........
متن کاملGeneric Vanishing Theory via Mixed Hodge Modules
We extend most of the results of generic vanishing theory to bundles of holomorphic forms and rank-one local systems, and more generally to certain coherent sheaves of Hodge-theoretic origin associated with irregular varieties. Our main tools are Saito’s mixed Hodge modules, the Fourier–Mukai transform for D-modules on abelian varieties introduced by Laumon and Rothstein, and Simpson’s harmonic...
متن کاملA Morphism of Intersection Homology and Hard Lefschetz
We consider a possibility of the existence of intersection homology morphism, which would be associated to a map of analytic varieties. We assume that the map is an inclusion of codimension one. Then the existence of a morphism follows from Saito’s decomposition theorem. For varieties with conical singularities we show, that the existence of intersection homology morphism is exactly equivalent ...
متن کاملOn the Brauer-Manin obstruction for zero-cycles on curves
We wish to give a short elementary proof of S. Saito’s result that the Brauer-Manin obstruction for zero-cycles of degree 1 is the only one for curves, supposing the finiteness of the Tate-Shafarevich-group X1(A) of the Jacobian variety. In fact we show that we only need a conjecturally finite part of the Brauer-group for this obstruction to be the only one. We also comment on the situation in ...
متن کامل