Advanced Topics in Algebraic Geometry - Wintersemester 2014/15

Dr. Eugen Hellmann
E-mail: hellmann (add

Tuesday, Thursday 10-12h, Seminarraum 0.006, Endenicher Allee 60
First lecture: 07.10.2014


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


The exams will take place on Thursday the 5th of February 2015.


  • 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