GRK 1800

This seminar is concerned to support the communication among thedoctoral students and to develop a scientific interaction with the scientists from the program.

The current outline of the seminar.

Plan of talks

15.10.2014:

Overview
B. Bakker

22.10.2014:

Triangulated categories
Generalities. Abelian categories. Homotopy category of complexes
(Huybrechts Chapters 1,2; Gelfand-Manin Chapter III,IV)

29.10.2014:

Complex tori
Cohomology. Riemann forms
(Mumford Chapter 1; Milne §2)

05.11.2014:

Derived categories
Derived categories of abelian categories
(Huybrechts Chapter 2; Gelfand-Manin Chapter III)

12.11.2014:

Abelian varieties
Definition. Rigidity. Theorem of the cube
(Polishchuk Chapter 8; Mumford Chapter II,III; Milne §1,4)

19.11.2014:

Derived categories of varieties
Serre functors. Reconstruction theorem
(Huybrechts Chapter 3,4)

26.11.2014:

Line bundles on abelian varieties
Projectivity. Line bundles I. Isogenies
(Polishchuk Chapter 8; Mumford Chapter II; Milne §5,6)

03.12.2014:

Exact functors
Derived functors. Fourier-Mukai transforms I
(Huybrechts Chapter 4)

10.12.2014:

The dual abelian variety
Construction of the dual
(Polishchuk Chapter 9; Milne §7)

17.12.2014:

Mukai's theorem
The Poincaré bundle. Line bundles II. Homogeneous bundles
(Polishchuk Chapter 11)

07.01.2015:

Orlov's criterion
Fourier-Mukai transforms II. Proof of Mukai's theorem
(Huybrechts Chapter 5)

14.01.2015:

The derived category of an elliptic curve
Stable sheaves. SL₂action
(Polishchuk Chapter 14)

21.01.2015:

Derived equivalences of abelian varieties I
(Huybrechts Chapter 9)

28.01.2015:

Derived equivalences of abelian varieties II
(Huybrechts Chapter 9)

04.02.2015:

Autoequivalences of abelian varieties
(Huybrechts Chapter 9)

11.02.2015:

Further topics

▷ GRK 1800 ▷ News ▷ Researchers ▷ College Seminar ▷ Intensive Courses ▷ Summer Schools ▷ Guests		International Research Training Group GRK 1800 College Seminar
		This seminar is concerned to support the communication among thedoctoral students and to develop a scientific interaction with the scientists from the program. Abelian varieties and Fourier-Mukai transforms Winter Semester 2014/15 The current outline of the seminar. Plan of talks 15.10.2014: Overview B. Bakker 22.10.2014: Triangulated categories Generalities. Abelian categories. Homotopy category of complexes (Huybrechts Chapters 1,2; Gelfand-Manin Chapter III,IV) 29.10.2014: Complex tori Cohomology. Riemann forms (Mumford Chapter 1; Milne §2) 05.11.2014: Derived categories Derived categories of abelian categories (Huybrechts Chapter 2; Gelfand-Manin Chapter III) 12.11.2014: Abelian varieties Definition. Rigidity. Theorem of the cube (Polishchuk Chapter 8; Mumford Chapter II,III; Milne §1,4) 19.11.2014: Derived categories of varieties Serre functors. Reconstruction theorem (Huybrechts Chapter 3,4) 26.11.2014: Line bundles on abelian varieties Projectivity. Line bundles I. Isogenies (Polishchuk Chapter 8; Mumford Chapter II; Milne §5,6) 03.12.2014: Exact functors Derived functors. Fourier-Mukai transforms I (Huybrechts Chapter 4) 10.12.2014: The dual abelian variety Construction of the dual (Polishchuk Chapter 9; Milne §7) 17.12.2014: Mukai's theorem The Poincaré bundle. Line bundles II. Homogeneous bundles (Polishchuk Chapter 11) 07.01.2015: Orlov's criterion Fourier-Mukai transforms II. Proof of Mukai's theorem (Huybrechts Chapter 5) 14.01.2015: The derived category of an elliptic curve Stable sheaves. SL₂action (Polishchuk Chapter 14) 21.01.2015: Derived equivalences of abelian varieties I (Huybrechts Chapter 9) 28.01.2015: Derived equivalences of abelian varieties II (Huybrechts Chapter 9) 04.02.2015: Autoequivalences of abelian varieties (Huybrechts Chapter 9) 11.02.2015: Further topics