Hochschild cohomology, complexity and support varieties

Abstract

This PhD-thesis consists of the five papers

- On the Hochschild (co)homology of quantum exterior algebras, to appear in Comm. Algebra,

-Complexity and periodicity, Coll. Math. 104 (2006), no. 2, 169-191,

-Twisted support varieties,

-Modules with reducible complexity, to appear in J. Algebra,

- On support varieties for modules over complete intersections, to appear in Proc. Amer. Math. Soc.

These papers are roughly divided into two groups; the ¯rst three study modules over Artin algebras using techniques from Hochschild cohomology, whereas the last two papers study modules over commutative Noetherian local rings, in particular modules over complete intersections.