Algebraic Geometry - Winter 2019/2020

* Lecture 1 - 7.10.2019. We discussed affine algebraic sets and stated Hilbert basis theorem.

* Lecture 2 - 14.10.2019. We proved Hilbert basis theorem, and showed affine algebraic varieties corresponds to prime ideals.

* Lecture 3 - 21.10.2019. Polynomial functions, coordinate rings, introduction to category theory.

* Lecture 4 - 4.11.2019. The functor we constructed from affine algebraic sets to finitely generated K-algebras is fully faithful. The rational function field.

* Lecture 5 - 11.11.2019. Bijection between rational maps with dense image and homomorphisms of fields of rational functions. Localization and the spectrum of a ring.

* Lecture 6 - 18.11.2019. More on localization. The topology of affine schemes. Radical ideals.

* Lecture 7 - 25.11.2019. The Hilbert Nullstellensatz and its applications.

* Lecture 8 - 2.12.2019. More on local rings, discrete valuation rings.

* Lecture 9 - 9.12.2019. Introduction to projective geometry.

* Lecture 10 - 16.12.2019. Sheaves, prevarieties, varieties, more on projective geometry.


* Exercise 1 - pdf.

* Exercise 2 - pdf.

* Exercise 3 - pdf.

* The final exam will take place on Wednesday, 15.01.2020, between 14:00 and 17:00 at room K7.