Advanced Topics in Algebraic Geometry - Wintersemester 2014/15
Dr. Eugen Hellmann
E-mail: hellmann (add @math.uni-bonn.de)
Tuesday, Thursday 10-12h, Seminarraum 0.006, Endenicher Allee 60
First lecture: 07.10.2014
Contents
The lecture builds on the course Algebraic Geometry II . Some of the topics that will be covered are:
- More on the cohomology of (quasi-)coherent sheaves
- Serre duality
- Cohomology and base changes, and applications
- Curves and families of curves
- Curves over algebraically closed fields and their embeddings into projective spaces
- Relative curves and families of (very) ample line bundles
- Formal schemes
- Basic definitions; completion of schemes along closed subschemes
- Coherent sheaves on formal schemes
- Formal GAGA
- Lifting curves to characteristic zero
Exams
The exams will take place on Thursday the 5th of February 2015.
References
- B. Fantechi et. al. Fundamental Algebraic Geometry: Grothendieck's FGA Explained
- A. Grothendieck, J. Dieudonné: Éléments de Géométrie Algébrique I-IV, Publ. Math. IHES
- R. Hartshorne : Algebraic Geometry, Springer
Last modified: 21. 01. 2015, Eugen Hellmann