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arXiv · 2008.07158

Homological theory of $k$-idempotent ideals in dualizing varieties

Luis Gabriel Rodríguez Valdés·Valente Santiago Vargas·Martha Lizbeth Shaid Sandoval Miranda
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Abstract

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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Luis Gabriel Rodríguez Valdés, Valente Santiago Vargas, Martha Lizbeth Shaid Sandoval Miranda. 2020-08-17. Homological theory of $k$-idempotent ideals in dualizing varieties. https://arxiv.org/abs/2008.07158

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