MAT-646

Algebraic geometry studies the solutions to systems of polynomial equations in several variables. Schemes are an important part of the modern foundations of the subject. Schemes provide a much tighter and more powerful connection between algebra (commutative rings and modules) and geometric and topological objects (varieties, manifolds) and simplify the use of modern techniques like cohomology.

This course is an introduction to the theory of schemes and will cover sheaves, affine schemes, projective and general schemes, morphisms, and geometric concepts like dimension and regularity as time permits.

Students will learn to apply algebraic concepts from introductory courses systematically in a throughly general context. This is a high-level training of abstract thinking in modern mathematics as well as useful preparation for further study in algebra and algebraic geometry.

Benotete Modulprüfung

Active and successful participation in the problem sessions (Übungen). Details to be announced by the instructor at the beginning of the course.

Oral exam (approx. 30 minutes). In exceptional cases written exam (120-180 minutes)

Linear Algebra, Algebra I

1. Wahlpflichtmodul für Master Mathematik, Master Technomathematik, Master Wirtschaftsmathematik
2. Reine Mathematik