对偶簇中$k$ -幂等理想的同调理论
Homological theory of $k$-idempotent ideals in dualizing varieties
摘要：
本文在对偶簇的背景下发展了$k$ -幂等理想的理论。M. Auslander，M. I. Platzeck和G.托多罗夫是扩展到这方面。给定一个理想$\mathcal{I}$（它是一个投射模的迹），我们构造了一个典型的平行元，它类似于Artin代数上模范畴中的一个著名的平行元.此外，我们还研究了这类元所涉及范畴的同调性质。因此，我们找到了理想$\mathcal{I}$上的条件，得到了在这样一个元中的拟遗传代数。有界导出范畴的应用也给出了。
英文摘要：
In this work, we develop the theory of $k$-idempotent ideals in the setting of dualizing varieties. Several results given previously in \cite{APG} by M. Auslander, M. I. Platzeck, and G. Todorov are extended to this context. Given an ideal $\mathcal{I}$ (which is the trace of a projective module), we construct a canonical recollement which is the analog to a well-known recollement in categories of modules over artin algebras. Moreover, we study the homological properties of the categories involved in such a recollement. Consequently, we find conditions on the ideal $\mathcal{I}$ to obtain quasi-hereditary algebras in such a recollement. Applications to bounded derived categories are also given.
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