Crepant resolutions and noncommutative algebra

Michel Van den Bergh

It is quite clear nowadays that among resolutions of singularities it is very natural to include some mild non-commutative ones. I will discuss some examples of this phenomenon and I will show that these examples form a nice complement to the Bondal-Orlov-conjecture which states that all crepant resolutions of a singularity have the same derived category.