Characteristic-p Methods.
Instructor: Manoj Kummini.

Plan of lectures (this will change as the course progresses.):

Tue 2016-01-05: Outline of the proof of the Hochster-Roberts' theorem 
Wed 2016-01-06: No lecture
Thu 2016-01-07: No lecture

Tue 2016-01-12: Hochster-Roberts, ctd.
Wed 2016-01-13: No lecture
Thu 2016-01-14: No lecture

Tue 2016-01-19: Hochster-Roberts, ctd.
Wed 2016-01-20: Koszul complexes
Thu 2016-01-21: Auslander-Buchsbaum formula, Regular local rings

Tue 2016-01-26: No lecture (CMI holiday) 
Wed 2016-01-27: Injective modules, Matlis duality
Thu 2016-01-28: Injective modules, Matlis duality, ctd.

Tue 2016-02-02: Cohen-Macaulay and Gorenstein rings
Wed 2016-02-03: Cohen-Macaulay and Gorenstein rings, ctd.
Thu 2016-02-04: Local cohomology

Tue 2016-02-09: Local cohomology, ctd.
Wed 2016-02-10: F-purity, F-splitting, F-injectivity 
Thu 2016-02-11: Generic freeness theorem.

Tue 2016-02-16: Reduction to characteristic p.
Wed 2016-02-17: Revisit the proof of Hochster-Roberts
Thu 2016-02-18: Tight closure: basic properties


Tue 2016-02-23: No lecture (midterm exams week)
Wed 2016-02-24: No lecture (midterm exams week) 
Thu 2016-02-25: No lecture (midterm exams week)

Tue 2016-03-01 - Thu 2015-04-21: To be decided 
Thu 2016-04-14: No lecture (CMI holiday)


Wed 2016-03-02
Thu 2016-03-03
Tue 2016-03-08
Wed 2016-03-09
Thu 2016-03-10
Tue 2016-03-15

F-rational and F-regular rings
F-rationality in terms of local cohomology
F-rationality implies pseudo-rationality 
projective varieties, section rings
F-splitting of projective varieties and the F-purity of section rings
Kodaira vanishing theorem.