Hypersurface support and prime ideal spectra for stable categories

Abstract

We use hypersurface support to classify thick (two-sided) ideals in the stable categories of representations for several families of finite-dimensional integrable Hopf algebras: bosonized quantum complete intersections, quantum Borels in type $A$, Drinfeld doubles of height 1 Borels in finite characteristic, and rings of functions on finite group schemes over a perfect field. We then identify the prime ideal (Balmer) spectra for these stable categories. In the curious case of functions on a finite group scheme $G$, the spectrum of the category is identified not with the spectrum of cohomology, but with the quotient of the spectrum of cohomology by the adjoint action of the subgroup of connected components ${\pi }_0(G)$ in $G$.

arXiv comment43 pages, minor changes to the presentation

References in corpus (8)

• Higher Topos Theory
• Frobenius-Schur Indicators and Exponents of Spherical Categories
• The tensor structure on the representation category of the ${\mathcal{W}}_p$ triplet algebra
• Subcategories of singularity categories via tensor actions
• Cohomology for Drinfeld doubles of some infinitesimal group schemes
• Tensor Triangular Geometry for Quantum Groups
• On Two Invariants of Three Manifolds from Hopf Algebras
• Balmer spectra and Drinfeld centers

Cited by in corpus (2)

• On the spectrum and support theory of a finite tensor category
• Support theory for Drinfeld doubles of some infinitesimal group schemes