Professor A.J. de Jong, Columbia university, Department of Mathematics.

** Introduction.**
Grothendieck in SGA2 found a marvellous approach to coherent cohomology
and Lefschetz theorems using dualizing complexes. We will revisit some
of these results mostly in a purely algebraic setting.
Here are some topics we will discuss:

- derived completion
- local cohomology
- complete vs torsion
- dualizing complexes
- local duality theorem
- annihilators of local cohomology
- finiteness theorem

Organizational:

- This semester I will give the lectures myself, so there is no need to sign up for lectures.
- Please email me if you want to be on the associated mailing list.
- Time and place: Room 407, Fridays 10:30 -- 12:00 AM.
- First meeting: January 19. Everybody interested please attend.

Related discussion in Stacks project:

- Derived completion 091N 0BKF 0BKH (Lecture 1)
- Local Cohomology 0BJA 0952 0BJD (Lecture 2)
- Complete vs Torsion 0A6V (Lecture 2)
- Dualizing Complexes 0A7A 0A7M 0A7W (Lecture 3)
- Local duality 0A81 (Lecture 3)
- Annihilators of local cohomology 0EFB (Lecture 4)
- Finiteness theorem 0AW7 0BJQ (Lecture 4)
- Completion of local cohomology modules and ML 0EEW 0EEX 0EFN (will be in lecture Friday 2-16)
- Algebraization of local cohomology 0EFF first 0EFP second (local) 0EFT bootstrap
- Algebraization of formal sections 0DXH 0EG1
- Algebraization of coherent formal modules 0DXS
- Discussion of applications and further results.

References:

- Grothendieck, SGA 2
- Mme Mich\`ele Raynaud, Theoremes de Lefschetz en cohomologie coherente et en cohomologie etale, Memoire de la SMF
- Faltings, A contribution to the theory of formal meromorphic functions, Nagoya Math J
- Faltings, Der Endlichkeitssatz in der localen Kohomologie, Math Ann
- Faltings, Algebraization of Some Formal Vectorbundles, Annals of Math
- Faltings, Uber die Annulatoren lokaler Kohomologiegruppen, Arch Math
- Faltings, Erganzungen zu einem Artikel uber dualizierende Komplexe, Arch Math
- Faltings, Some Theorems about Formal Functions, Publ RIMS
- Faltings, Uber lokale Kohomologiegruppen hoher Ordnung, Journal fur die reine und angewandte Mathematik
- Faltings, Zur Existenz dualisierender Komplexe, Math Z