Cours fondamental 2 (GA)

Schémas II : faisceaux cohérents et cohomologie

Maria Yakerson (Travaux dirigés par Quentin Gazda)

Contact : yakerson à imj-prg.fr

Pas de notes de cours prévues.

Langue du cours : anglais

Présentation

This course is a continuation of the course Schemes I. It focuses on the cohomology of coherent sheaves, which is a fundamental invariant of schemes and important tool in algebraic geometry. We will construct the theory of sheaf cohomology and establish its fundamental properties. In the end we will explore some applications of this theory.

Contenu

• coherent sheaves
• cohomology of coherent sheaves
• characterization of affine schemes
• Serre duality
• applications

Prérequis

Bibliographie

• Ravi Vakil. Foundations of Algebraic Geometry. https://math.stanford.edu/~vakil/216blog/FOAGfeb2124public.pdf
• Qing Liu. Algebraic Geometry and Arithmetic Curves.
• Geir Ellingsrud and John Christian Ottem. Introduction to schemes. https://www.uio.no/studier/emner/matnat/math/MAT4215/data/masteragbook.pdf
• U. Goertz, T. Wedhorn. Algebraic Geometry II: Cohomology of Schemes.
• R. Hartshorne. Algebraic Geometry.