Mathematical Institute of the University of Bonn

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