In mathematics, the direct image functor is a construction in sheaf theory that generalizes the global sections functor to the relative case. Definition · Variants · Properties

1 апр. 2021 г. · A sheaf on Y should be defined on some open subset of Y and gives as some nice function(holomorphic,....) on that open subset. Stalks and direct image - Mathematics Stack Exchange A proposition about direct image sheaves - Math Stack Exchange Другие результаты с сайта math.stackexchange.com

24 дек. 2020 г. · This page is about direct images of sheaves and related subjects. For the set-theoretic operation, see image. Idea · Definition · Examples · Direct image with compact...

We claim that the direct image of a sheaf is a sheaf. Namely, if \{ V_ j \to V\} is an étale covering in Y_{\acute{e}tale} then \{ X \times _ Y V_ j \to X ...

5 окт. 2006 г. · The relative version of cohomology of a sheaf is the higher direct image of the sheaf (taken over SpecZ this yields the usual cohomology groups) ...

23 апр. 2010 г. · Is the direct image of the structure sheaf on X isomorphic to the structure sheaf on Y when X->Y is flat and proper with connected fibers ...

Let X and S be noetherian schemes, and OX (resp. OS) the structure sheaf of X (resp. S). Let f : X → S be a morphism of schemes.

In this section we prove the fundamental fact that the higher direct images of a coherent sheaf under a proper morphism are coherent. Proposition ...

For example the direct image is dual to the direct image with compact support. This phenomenon is studied and used in the theory of perverse sheaves. Base ...