Mathematical Institute of the University of Bonn

Algebraic Geometry II - Sommersemester 2014

Dr. Eugen Hellmann
E-mail: hellmann (add @math.uni-bonn.de)

Monday 12-14h, Thursday 10-12h, Kleiner Hörsaal, Wegelerstraße 10
First lecture: 07.04.2014

Contents

The lecture builds on the course Algebraic Geometry I and continuos the study of schemes and their properties. The provisional schedule includes:

• Global and local properties of morphisms:
• global properties: affine and projective morphisms; separated and proper morphisms; the valuative criteria;
• local properties: ètale, smooth and unramified morphisms; infinitesimal lifting criteria
• Formal schemes
• basic definitions; completion of schemes along closed subschemas
• coherent sheaves on formal schemes
• formal GAGA
• Cohomology of (quasi-)coherent sheaves
• derived functor cohomology and Čech cohomology
• Higher direct images; cohomology and base changes; applications
• Serre duality

Exercise sessions

There are weekly exercise sessions accompanying the lecture. It is necessary to attend the exercise sessions and hand in the exercise sheets in order to participate in the final exam.
The exercise sessions take place on Fridays, 10-12h, Romm 0.008.

Exercise sheets

• Exercise sheet 1 due 24.04.2014
• Exercise sheet 2 due 05.05.2014
• Exercise sheet 3 due 12.05.2014
• Exercise sheet 4 due 19.05.2014
• Exercise sheet 5 due 26.05.2014
• Exercise sheet 6 due 02.06.2014
• Exercise sheet 7 due 16.06.2014
• Exercise sheet 8 due 23.06.2014
• Exercise sheet 9 due 30.06.2014
• Exercise sheet 10 due 07.07.2014

Exercise sessions

The oral exams will take place in the last week of the semester and the first week of the holidays.

References

• U. Görtz, T. Wedhorn: Algebraic Geometry I , Springer Vieweg
• A. Grothendieck, J. Dieudonné: Éléments de Géométrie Algébrique I-IV, Publ. Math. IHES
• R. Hartshorne : Algebraic Geometry, Springer
• D. Mumford: The Red Book of Varieties and Schemes, Springer

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Last modified: 30. 06. 2014, Eugen Hellmann