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Algebraic Geometry in Positive Characteristic - NMIB013

Title:	Algebraická geometrie v kladné charakteristice
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2013 to 2017
Semester:	summer
E-Credits:	6
Hours per week, examination:	summer s.:4/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. RNDr. Petr Somberg, Ph.D.
Classification:	Mathematics > Algebra
Interchangeability :	NMAG436
Is incompatible with:	NMAG436
Is interchangeable with:	NMAG436

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Annotation -

Last update: T_KA (17.05.2003)

The course developes basic concepts of algebraic geometry and curve theory, both over general fields and over finite fields.

Literature - Czech

Last update: T_KA (23.05.2003)

R. Hartshorne: Algebraic geometry, Springer-Verlag 1977;

J.W.P.Hirschfeld: Projective geometries over finite fields, Clarendon Press 1988.

Syllabus -

Last update: T_KA (23.05.2003)

Affine and projective algebraic sets and varieties, function fields, singularities, homogenization, affine and projective closure. Morphisms of varieties and curves, rational maps of curves and their degree, separability and pure inseparability. Frobenius map. Group of divisors, Riemann-Roch and Hurwitz Theorem. Genus of a curve. Number of points on a curve: Hasse-Weil and Stöhr-Voloch Theorem.