Institut für Mathematik       Universität Zürich | ||
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Lecture notes
Here you find lecture notes for the second half of the course: version: 28th May 2020Board diary (for the second half of the course)
Date | Content |
07.04. | Motivation for cohomology, abelian categories, injective objects, sheaves have enough injectives |
21.04. | Existence and properties of right-derived functors |
23.04. | Derived functors via F-acyclic resolutions, injective abelian groups |
28.04. | Projective objects, left-derived functors, enough projective sheaves on finitely generated spaces, sheaf cohomology |
30.04. | Flasque sheaves are acyclic, cohomology on open/closed subspaces, Mayer-Vietoris sequences |
05.05. | Godement resolution, Čech cohomology |
07.05. | Čech cohomology equals sheaf cohomology on paracompact spaces, first cohomology on good covers |
12.05. | an example, first cohomology in terms of torsors |
14.05. | Higher direct images, homotopy invariance of sheaf cohomology |
19.05. | Sheaves in terms of étalé spaces, étalé spaces of locally constant sheaves |
21.05. | complements on (locally) constant sheaves, fundamental groupoid and its monodromy representation |
26.05. | equivalence of the monodromy functor, classification of locally constant sheaves on spheres and on the torus |
28.05. | alternative proof of homotopy invariance of sheaf cohomology for locally constant sheaves, outlook |