Material for the course on Algebraic D-modules (fall 2008).
The course meets Monday, Wednesday 9:30--11 at 2-135.
Homework 1, due 9/24.
Homework 2, due 10/15.
Homework 3, due 10/29.
Homework 4, due 11/17.
The book by A. Borel "Algebraic D-modules" contains much of what will be
covered in the first half of the course.
The book by Kashiwara "D-modules and microlocal calculus" emphasizes the role
Malgrange's Bourbaki talk from 1977/78 (LNM 710) gives a nice explanation
of microlocalization and involutivity of the singular support.
Bersntein's notes is a very good, albeit concise, exposition of the
key results including application to Kazhdan-Lusztig conjectures.
A course by
J.-P.Schneiders explains some of the basic constructions.
A recent book "D-modules, perverse sheaves and representation theory" by
Hotta, Takeuchi and Kashiwara touches upon most of the topics of
!-crystals are discussed in section 7 (pp 284--298) of the
"Quantization of Hitchin's integrable system and Hecke eigensheaves"
by Beilinson and Drinfeld available at their
(References as of October 2008).
contains further links. By the way, his paper with Nevins
(JAMS 17 (2004) 155-179) shows that various definitions of D-modules
agree sometimes even for singular varieties.
In the discussion of Kazhdan-Lusztig conjectures I followed
MacPherson's argument described in the Bourbaki talk
Quelques applications de la cohomologie d'intersection
by T. Springer. See also Soergel's ICM (1994) talk "Gradings on
representation categories" for a discussion of grading on categories and
its relation to Kazhdan-Lusztig conjectures.
The definition of unipotent nearby cycles was introduced in
Beilinson's paper who to glue perverse sheaves, a typed version
can be found here.
A discussion of b-functions and multiplier ideals appears
in recent papers of Budur
and Budur, Saito.