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Abstract
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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
, Drinfeld doubles
of height
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
, 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
in
.
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Keywords
tensor triangular geometry, Balmer spectrum, quantum
groups, quantum complete intersections
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Mathematical Subject Classification
Primary: 16E30, 16T05, 18G80, 18M05
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Milestones
Received: 26 August 2021
Revised: 31 August 2022
Accepted: 6 November 2022
Published: 1 May 2023
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© 2023 MSP (Mathematical Sciences
Publishers). |
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