Abstract:

The classical representation scheme Rep_n(A), parametrizing the n-dimensional representations of an associative algebra A, defines a (non-additive) functor on the category of associative algebras. A natural problem is to describe the higher derived functors of Rep_n in the sense of non-abelian homological algebra.

I. Ciocan-Fontanine and M. Kapranov (2002) proposed a geometric solution to this problem as part of a general program of deriving Quot schemes and other moduli spaces in algebraic geometry. In this talk, I will present a different, more explicit construction of the derived functors of Rep_n arising from noncommutative geometry and discuss some interesting implications.