- theory of schemes (affine, projective and relative schemes),
- structure sheaves and sheaves of modules,
- flat families,
- Grothendieck functor.
Geometry of Schemes (M, 4.5 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-42-13-M-7||Geometry of Schemes||4.5 CP (135 h)|
|CP, Effort||4.5 CP = 135 h|
|Position of the semester||1 Sem. irreg.|
|Level|| Master (Advanced)|
|Area of study||[MAT-AGCA] Algebra, Geometry and Computer Algebra|
|Reference course of study||[MAT-88.105-SG] M.Sc. Mathematics|
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
Geometry of Schemes
|P||28 h||107 h||-||-||PL1||4.5||irreg.|
- About [MAT-42-13-K-7]: Title: "Geometry of Schemes"; Presence-Time: 28 h; Self-Study: 107 h
Examination achievement PL1
- Form of examination: oral examination (20-30 Min.)
- Examination Frequency: irregular (by arrangement)
- Examination number: 86237 ("Geometry of Schemes")
Evaluation of grades
The grade of the module examination is also the module grade.
Competencies / intended learning achievements
They are able to name the essential propositions of the lecture as well as to classify and to explain the connections. They understand the proofs presented in the lecture and they are able to reproduce and explain them. In particular, they can critically assess what conditions are necessary for the validity of the statements.
- D. Eisenbud, J. Harris: The Geometry of Schemes,
- H. Matsumura: Commutative Ring Theory,
- R. Hartshorne: Algebraic Geometry.
Requirements for attendance (informal)
- [MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)
- [MAT-40-11-M-4] Commutative Algebra (M, 9.0 LP)
- [MAT-40-12-M-7] Algebraic Geometry (M, 9.0 LP)