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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
4EU+:	no
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

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

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.

Last update: G_M (28.05.2012)

Literature -

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

Last update: G_M (28.05.2012)

Syllabus -

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.

Last update: G_M (28.05.2012)

Entry requirements -

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

Last update: G_M (28.05.2012)