Hypersurface support for noncommutative complete intersections
Abstract
We introduce an infinite variant of hypersurface support for finite-dimensional, noncommutative complete intersections. By a noncommutative complete intersection we mean an algebra R which admits a smooth deformation Q R by a Noetherian algebra Q which is of finite global dimension. We show that hypersurface support defines a support theory for the big singularity category Sing(R), and that the support of an object in Sing(R) vanishes if and only if the object itself vanishes. Our work is inspired by Avramov and Buchweitz' support theory for (commutative) local complete intersections. In a companion piece, we employ hypersurface support, and the results of the present paper, to classify thick ideals in stable categories for a number of families of finite-dimensional Hopf algebras.