Section 3.8 - Higher Direct Images of Sheaves
نویسنده
چکیده
In this note we study the higher direct image functors Rf∗(−) and the higher coinverse image functors Rf (−) which will play a role in our study of Serre duality. The main theorem is the proof that if F is quasi-coherent then so is Rf∗(F ), which we prove first for noetherian schemes and then more generally for quasi-compact quasi-separated schemes. Most proofs are from either Hartshorne’s book [1] or Kempf’s paper [2], with some elaborations.
منابع مشابه
Sheaf Cohomology Course Notes, Spring 2010
Overview 1 1. Mymotivation: K-theory of schemes 2 2. First steps in homological algebra 3 3. The long exact sequence 6 4. Derived functors 8 5. Cohomology of sheaves 10 6. Cohomology of a Noetherian Affine Scheme 12 7. Čech cohomology of sheaves 12 8. The Cohomology of Projective Space 14 9. Sheaf cohomology on P̃2 16 10. Pushing around sheaves, especially by the Frobenius 17 11. A first look at...
متن کاملHigher Direct Images of Dualizing Sheaves of Lagrangian Fibrations
We prove that the higher direct images of the dualizing sheaf of a Lagrangian fibration between smooth projective manifolds are isomorphic to the cotangent bundles of base space. As a corollary, we obtain that every Hodge number of the base space of a fibre space of an irreducible symplectic manifold is the same to that of a projective space if the base space is smooth.
متن کاملGraded Duality for Filtered D-modules
For a coherent filtered D-module we show that the dual of each graded piece over the structure sheaf is isomorphic to a certain graded piece of the ring-theoretic local cohomology complex of the graded quotient of the dual of the filtered D-module along the zero-section of the cotangent bundle. This follows from a similar assertion for coherent graded modules over a polynomial algebra over the ...
متن کاملNotes on Character Sheaves
In the first section we study a functor of Bezrukavnikov, Finkelberg and Ostrik defined on character sheaves; we compute it in a Grothendieck group taking weights into account. In the second section we enlarge the class of character sheaves to a larger class of simple perverse sheaves which behaves well with respect to tensor product (unlike the character sheaves themselves). 2000 Math. Subj. C...
متن کاملPerverse sheaves on affine Grassmannians and Langlands duality
In this paper we outline a proof of a geometric version of the Satake isomorphism. Namely, given a connected, complex algebraic reductive group G we show that the tensor category of representations of the dual group G is naturally equivalent to a certain category of perverse sheaves on the affine Grassmannian of G. This can be extended to give a topological realization of algebraic representati...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006