Hochschild cohomology, complexity and support varieties
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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.