Material for the course on Algebraic D-modules (fall 2008).
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The course meets Monday, Wednesday 9:30--11 at 2-135.
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<a href="announce08.dvi">Course announcement.</a>

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<a href="hw1_08.dvi">Homework 1,</a> due 9/24.

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<a href="hw2_08.dvi">Homework 2,</a> due 10/15.
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<a href="hw3_08.dvi">Homework 3,</a> due 10/29.
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<a href="hw4_08.dvi">Homework 4,</a> due 11/17.
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<a href="hw5_08.dvi">Homework 5.</a> 
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Some references:
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The book by A. Borel "Algebraic D-modules" contains much of what will be
covered in the first half of the course.

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The book by Kashiwara "D-modules and microlocal calculus" emphasizes the role
of b-functions.

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Malgrange's Bourbaki talk from 1977/78 (LNM 710) gives a nice explanation
of microlocalization and involutivity of the singular support.

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<a 
href="http://www.math.uchicago.edu/~arinkin/langlands/Bernstein/Bernstein-dmod.ps">
Bersntein's notes</a> is a very good, albeit concise, exposition of the 
key results including application to Kazhdan-Lusztig conjectures.

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<a href="http://www.ulg.ac.be/analg/jps/idm.pdf">A course by 
J.-P.Schneiders</a> explains some of the basic constructions. 

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A recent book "D-modules, perverse sheaves and representation theory" by
Hotta, Takeuchi and Kashiwara touches upon most of the topics of
the course.

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<i> !-crystals </i> are discussed in section 7 (pp 284--298) of the 
unfinished book 
"Quantization of Hitchin's integrable system and Hecke eigensheaves"
by Beilinson and Drinfeld available at their
<a href="http://www.math.uchicago.edu/~mitya/langlands.html"> seminar page. </a>
(References as of October 2008). 

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<a href="http://www.math.utexas.edu/~benzvi/Langlands.html">Ben-Zvi's 
page</a> 
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.



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In the discussion of Kazhdan-Lusztig conjectures I followed 
MacPherson's argument described in the Bourbaki talk 
<a 
href="http://www.numdam.org/numdam-bin/item?id=SB_1981-1982__24__249_0">
Quelques applications de la cohomologie d'intersection </a>
 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.

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The definition of unipotent nearby cycles was introduced in 
Beilinson's paper who to glue perverse sheaves, a typed version
can be found <a href="http://www.math.harvard.edu/~ryanr/"> here. </a>

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A discussion of b-functions and multiplier ideals appears
in recent papers of <a href="http://arxiv.org/abs/math/0305247"> Budur </a>
and <a href="http://arxiv.org/abs/math/0305118"> Budur, Saito. </a>