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Course, academic year 2023/2024
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Geometry of Schemes - NALG132
Title: Geometrie schémat
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. RNDr. Jan Šťovíček, Ph.D.
Classification: Mathematics > Algebra
Annotation -
Last update: T_KA (20.05.2010)
This is an introductory lecture to the theory of schemes, a powerful tool which connected classical algebraic geometry to number theory and made it possible to resolve several hard problems. The concepts in the lecture will be illustrated on examples.
Literature -
Last update: T_KA (20.05.2010)

[1] D. Eisenbud, J. Harris: Geometry of Schemes, Springer-Verlag, New York, 2000.

[2] R. Hartshorne: Algebraic Geometry, Springer-Verlag, New York-Heidelberg, 1977.

Syllabus -
Last update: T_KA (20.05.2010)

1. Spectrum of a ring, affine schemes

2. Schemes in general

3. Morphisms of schemes, related constructions on schemes

4. Projective schemes, invariants

The contents of the lecture can be adjusted if there is demand to discuss more some topics from commutative algebra, or if there is an interest to look more in detail at examples.

Entry requirements -
Last update: T_KA (20.05.2010)

Some familiarity with basics of commutative algebra, properties of polynomial rings over a field and algebraic varieties.

 
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