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Course, academic year 2022/2023
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Algebraic and Analytic Geometry and the Theorem of J.-P. Serre - NALG137
Title: Algebraická a analytická geometrie a věta J.-P. Serra
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2014
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Guarantor: doc. RNDr. Jan Šťovíček, Ph.D.
Classification: Mathematics > Algebra
Annotation -
Last update: G_M (28.05.2012)
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: G_M (28.05.2012)

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

Syllabus -
Last update: G_M (28.05.2012)

The following will be explained during the lecture:

1. coherent sheaves as a generalization of vector bundles,

2. construction of projective spaces in the language of schemes,

3. translation of the J.-P. Serre theorem to sheaf cohomology and a proof of the cohomological version.

Entry requirements -
Last update: G_M (28.05.2012)

Basics of sheaves and the definition of an analytic manifold using sheaves. Some familiarity with the definition of complex schemes and their analytification.

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