Foundations of algebraic geometry - WS 2021/22

Instructor: Daniele Agostini.

Time and place: Monday, 11:15-12:45.
Room A3 01.

Important announcements

• The lecture of January 17 will take place from 17:00 to 18:30.
• Please subscribe to the mailing list of the course here.

Description

The idea of this reading group is to develop the basic notions of modern algebraic geometry, through the language of schemes.

Prerequisites: commutative algebra and algebraic geometry at an undegraduate level.

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References : We will follow closely the wonderful lecture notes by Vakil:

• R. Vakil, Foundations of Algebraic Geometry.

Other useful textbooks are:

• R. Hartshorne, Algebraic Geometry. Springer.
• Q. Liu, Algebraic Geometry and Arithmetic Curves. Oxford University Press.
• D. Eisenbud and J. Harris, The geometry of schemes . Springer.
• U. Görtz and T. Wedhorn, Algebraic Geometry I: Schemes . Springer.

The definitive references on the topic are:

• A. Grothendieck and J. Dieudonné, Éléments de géométrie algébrique. Publications Mathématiques de l'IHÉS.
• The Stacks project authors, The Stacks project.

Course log

A brief description of each session's content will appear below. There is also a tentative schedule of future sessions.

• 15 April 2021, 17-19. Presentation of the reading group (Daniele). Notes.
• 22 April 2021, 17-18. Vakil, Sections 1.1-1.2-1.3-1.4. After Section 1.3 do also the exercises here. (Chiara).
• 29 April 2021, 17-19. Vakil, Sections 1.5-1.6-2.1-2.2 (Claudia).
• 6 May 2021, 17-19. Vakil, Sections 2.3-2.4-2.5-2.6 (Oliver).
• 20 May 2021, 17-19. Vakil, Sections 3.1-3.2-3.3 (Yelena).
• 27 May 2021, 17-19. Vakil, Sections 3.1-3.2-3.3 (Yelena).
• 3 June 2021, 17-19. Vakil, Sections 3.4-3.5-3.6-3.7 (Mara).
• 10 June 2021, 17-19. Vakil, Sections 4.1-4.2-4.3 (Noah).
• 13 July 2021, 17-19. Vakil, Section 4.4 (Daniele).
• 22 July 2021, 17-19. Vakil, Sections 5.1-5.2 (Daniele).
• 5 August 2021, 17-19. Vakil, Sections 5.3-5.4 (Daniele).
• 12 August 2021, 17-19. Vakil, Section 5.5 (Daniele).
• 17 September 2021, 15-16. Vakil, Section 4.5 (Daniele).
• 7 October 2021, 17-19. Vakil, Sections 6.1-6.2-6.3 (Fulvio).
• 10 October 2021, 11-13. Vakil, Section 6.3 (all together without Daniele).
• 17 October 2021, 11-13. Vakil, Section 6.3 (Fulvio).
• 25 October 2021, 11-13. Vakil, Section 6.3 (Fulvio), Section 6.4 (Chiara).
• 5 November 2021, 15:30-17. Vakil, Sections 6.5-6.7 (Chiara).
• 8 November 2021, 11-13. Vakil, Sections 7.1-7.4 (Pedro).
• 15 November 2021, 11-13. Vakil, Sections 7.1-7.4 (Pedro).
• 22 November 2021, 11-13. Vakil, Sections 8.1-8.4 (Clemens).
• 29 November 2021, 11-13. Vakil, Sections 8.1-8.4 (Clemens).
• 12 December 2021, 15-17. Vakil, Sections 8.1-8.4 (Clemens).
• 17 December 2021, 17-19. Vakil, Sections 9.1-9.3 (Yassine).

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