<![CDATA[
<BODY>
MSRI Streaming Video Series <BR> Amnon Yekutieli
- The Auslander Condition and Perverse Sheaves
<BR> Abstract:
Perverse sheaves arose in the study of singular spaces (intersection cohomology). These are objects in the derived
category that behave like sheaves (for instance they can be glued). <p>
<p>
On an algebraic scheme the dualizing complex is a perverse sheaf. >From this, and using extra data (local duality
or rigidity), one can glue dualizing complexes inside the derived category.
<p>
Now let A be a noncommutative algebra, and let R be a dualizing complex over it. Suppose R satisfies the
Auslander condition. Then considering Mod A (the category of A-modules) as a space, R is a perverse sheaf.
<p>
We propose to use this observation to prove existence of dualizing complexes over A when localization is possible,
and also to make some headway towards duality for noncommutative schemes. (Joint work with J.J. Zhang.)
</BODY>
]]>