The course will usually take place on Mondays at 10:15-13:00 in Room 155 of the Ziskind Building in the Spring semester of 2018.
The exercise session by Shachar Carmeli will be on Tuesdays, 10:15 - 11 in Room 1.
We will start on March 19, and have ~14 meetings.
Prerequisites: Linear algebra and familiarity with commutative algebra and general topology.
The speed and the details level of the exposition of some basic topics will depend on the audience.
I will be giving exercises on almost every meeting. I will not force you to submit the exercises, but I encourage you to do so. Good grades for exercises can approve the final grade. We will have a take-home exam at the end of the course.
Syllabus:
Chapter I Affine schemes as ring spectra
Equations, rings, and ideals; Points of schemes and the Zariski topology; Hilbert's Nulstellensatz.
Chapter II. General Schemes
Sheaves; Affine schemes as ringed spaces; General schemes; Products of schemes; Projective schemes
Chapter III. Properties of morphisms
Finite morphisms; Separated morphisms; Proper morphisms and Chow's lemma; Valuation criteria;
If time permits: tangent spaces and tangent cones
Exercise 1
Exercise 2
Exercise 3
Exercise 4
Literature:
1. Eisenbud & Harris "The geometry of schemes"
2. Hartshorne "Algebraic Geometry"
3. Atiyah-Macdonalds "Introduction to commutative algebra"
4. Eisenbud "Commutative Algebra With a View Toward Algebraic Geometry"