Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-42-13-M-7

Geometry of Schemes (M, 4.5 LP)

Module Identification

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 [7] Master (Advanced)
Language [EN] English
Module Manager
Area of study [MAT-AGCA] Algebra, Geometry and Computer Algebra
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active


Type/SWS Course Number Title Choice in
Presence-Time /
SL SL is
required for exa.
PL CP Sem.
2V MAT-42-13-K-7
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.


  • theory of schemes (affine, projective and relative schemes),
  • structure sheaves and sheaves of modules,
  • flat families,
  • Grothendieck functor.

Competencies / intended learning achievements

Upon successful completion of this module, the students are familiar with the advanced language of schemes, which is used in the modern algebraic geometry. They are, thus, able to understand current works in geometry and arithmetics. They have studied typical examples and applications.

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.

References to Module / Module Number [MAT-42-13-M-7]

Module-Pool Name
[MAT-41-MPOOL-7] Specialisation Algebraic Geometry and Computer Algebra (M.Sc.)
[MAT-RM-MPOOL-7] Pure Mathematics (Advanced Modules M.Sc.)