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Seminar on sheaf theory

an_actual_sheaf

Florent Schaffhauser
Heidelberg University
Winter Semester 2022-2023

Organisation

The purpose of this seminar is to cover the basics of sheaf theory, with a view towards the cohomology of real and complex manifolds. The expositions will be given by the participants, in coordination with the professor in charge of running the seminar.

  • Target audience: Master students and advanced Bachelor students.
  • Language of instruction: English.
  • Time and place: 4-6pm on Wednesdays, in Seminar Room 8 (INF 205).

This seminar can be recommended as a complement to the course on Real Algebraic Varieties, taught in Heidelberg during the Winter Semester 2022-2023.

The equivalence between sheaves and étalé spaces

References

  1. B.R. Tennison, Sheaf Theory,  Cambridge University Press (1975).
  2. C. Voisin, Hodge Theory and Complex Algebraic Geometry: Volume I,  Cambridge University Press (2002).

Schedule

# Date Topic Speaker References Notes
1 05/10 Introductory meeting Florent Schaffhauser Syllabus
2 19/10 Presheaves and sheaves Anna Roth [Tennison]
§ 1, 2.1, 2.2
3 26/10 The sheafification of a presheaf Immanuel Klevesath [Tennison]
§ 2.3, 2.4
4 02/11 Covering spaces and locally constant sheaves Florent Schaffhauser
5 09/11 Morphisms of presheaves and sheaves Felix Preu [Tennison]
§ 3.2-3.4, 3.6
6 16/11 Ringed spaces and manifolds Till Janke [Tennison]
§ 4.1, 4.3
7 23/11 Locally free sheaves and invertible sheaves Elia Fiammengo [Tennison]
§ 4.4, 4.5
8 30/11 An introduction to the Riemann-Hilbert correspondence Florent Schaffhauser
9 07/12 Derived functors Tim Wagemann [Tennison]
§ 5.1, 5.2
10 14/12 Sheaf cohomology Mario Bühler [Tennison]
§ 5.3
11 11/01 Čech cohomology and the Picard group Aarya Shah [Tennison]
§ 5.4
12 18/01 Flabby, soft and fine sheaves Theresa Häberle [Voisin]
§ I.4
13 25/01 Cohomology of manifolds Matilde Sciortino [Voisin]
§ I.4
14 01/02 The Hodge decomposition theorem Florent Schaffhauser [Voisin]
§ II.5, II.6