SoSe 26 Seminar: Cohomology of sheaves and schemes

Time and place: Wednesday 16-18 M104

(A detailed program will appear soon)

In this seminar, we will introduce the cohomology of sheaves on topological spaces and schemes following Chapter III of Hartshorne. Beyond the definitions and basic properties of sheaf cohomology, we will compute the cohomology of affine schemes and projective spaces, and we will discuss the Serre duality theorem for projective schemes and its connection to the residue theorem in complex analysis. The first five talks are about sheaves on topological spaces and do not require any background in algebraic geometry. The rest assumes some basic knowledge of schemes (e.g., from Algebraic Geometry I or Chapter II of Hartshorne).

The distribution of talks will happen during the first meeting of the semester. You can also send me an email beforehand to reserve a talk.

Date	Speaker	Topic
15.04	Marc Hoyois	Introduction
22.04		Derived functors I: Construction
29.04		Derived functors II: Universal property
06.05		Cohomology of sheaves
13.05		Čech cohomology
20.05	—	—
27.05		Grothendieck vanishing
03.06		Cohomology of affine schemes
10.06		Serre’s affineness criterion and cohomology of separated schemes
17.06		Cohomology of projective spaces
24.06		Serre vanishing
01.07		Ext groups and sheaves
08.07	Antonin Milesi	Serre duality I: projective spaces and dualizing sheaves
15.07	Andrea Taccani	Serre duality II: Cohen-Macaulay schemes and local complete intersections