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Course, academic year 2023/2024
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Algebraic and Analytic Geometry - NALG127
Title: Algebraická a analytická geometrie
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, 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 (18.05.2011)
The aim of the course is to give the students an idea of the theorem of J.-P. Serre (and its proof) relating algebraic and analytic geometry.
Literature -
Last update: T_KA (18.05.2011)

A. Neeman, Algebraic and Analytic Geometry, Cambridge University Press, 2007.

Syllabus -
Last update: T_KA (18.05.2011)

The following will be explained during the lecture:

1. an algebraic approach to analytic manifolds using shaves,

2. schemes of finite type over the field of complex numbers as a

generalization of algebraic varieties,

3. the passage from schemes to complex analytic manifolds,

4. coherent sheaves as an algebraic incarnation and generalization of vector bundles,

5. the statement of Serre's GAGA theorem (Geometrie algebraique et geometrie analytique) and an attempt to prove it.

Entry requirements -
Last update: T_KA (18.05.2011)

Familiarity with basics of commutative algebra and elementary topology.

 
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