Support for Integrable Hopf Algebras via Noncommutative Hypersurfaces

Abstract We consider finite-dimensional Hopf algebras $u$ that admit a smooth deformation $U\to u$ by Noetherian algebra $U$ of finite global dimension. Examples such include small quantum groups over the complex numbers, restricted enveloping in characteristic, and Drinfeld doubles height $1$ group schemes. provide means analyzing (cohomological) support for representations $u$, via singularity categories hypersurfaces $U/(f)$ associated with functions $f$ on corresponding parametrization space. use this hypersurface approach to establish tensor product property cohomological support, following examples: scheme, certain 1 solvable schemes, bosonized complete intersections, Borel type $A$.