(in Polish) Zaawansowane narzędzia geometrii algebraicznej 1000-1M21ZNG
The first half will roughly consist of
(1) recap about flat and smooth morphisms,
(2) cohomology and base change theorem and applications,
(3) the theorem on formal function, Zariski's Main Theorem and Stein factorization
(4) Serre's duality and applications,
(5) Kodaira's vanishing theorem.
The second half will consists of participants' choices among several possible directions (e.g. Artin's approximation or introduction to stacks).
Type of course
Learning outcomes
the student knows the above mentioned theorems and is able to apply them in nontrivial situations, appropriately modifying the assumptions.
Assessment criteria
a part of the exercise sessions will be devoted to attendies' lectures. The final grade will depend on those and on the final oral exam.
Bibliography
given at the homepage. In the first half, we will follow R. Vaki's "Foundations of algebraic geometry"
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: