Hypersurface support and prime ideal spectra for stable categories
Hypersurface support and prime ideal spectra for stable categories
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DOI：
10.2140/akt.2023.8.25
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发表时间：
2021-01
影响因子：
0.6
通讯作者：
C. Negron;J. Pevtsova
中科院分区：
文献类型：
--
作者：
C. Negron;J. Pevtsova
我们使用超曲面支持对几个有限维可积 Hopf 代数族的表示的稳定类别中的厚（两侧）理想进行分类：玻色量子完全交集、$A$ 类型中的量子 Borels、有限特征中高度为 1 Borels 的 Drinfeld 双精度以及完美域上有限群方案上的函数环。然后，我们确定这些稳定类别的主要理想（巴尔默）光谱。在有限群方案$G$上的函数的奇怪情况中，类别的谱不是用上同调谱来识别的，而是用$G$中连通分量子群$\pi_0(G)$的伴随作用来用上同调谱的商来识别。
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 $G$.