Abstract
We introduce the notion of big tilting complexes over associative rings, which is a simultaneous generalization of good tilting modules and tilting complexes over rings. Given a two-term big tilting complex over an arbitrary associative ring, we show that the derived module category of its (derived) endomorphism ring is a recollement of the one of the given ring and the one of a universal localization of the endomorphism ring. This recollement generalizes the one established for a good tilting module of projective dimension at most one.
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Acknowledgements
Part of this work was written during the author’s study at Capital Normal University. The author takes this opportunity to express his sincere thanks to Prof. Changchang Xi for his kind and helpful supervision.
Funding
The research of the author was supported by research ability improvement program of BUCEA(Grant No.X22026) and Beijing Nova Program (Grant No.Z181100006218010).
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Huabo Xu wrote the full manuscript text.
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Xu, H. Recollements of Derived Categories from Two-Term Big Tilting Complexes. Algebr Represent Theor 27, 1267–1285 (2024). https://doi.org/10.1007/s10468-024-10258-w
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DOI: https://doi.org/10.1007/s10468-024-10258-w