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Partial silting objects and smashing subcategories

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Abstract

We study smashing subcategories of a triangulated category with coproducts via silting theory. Our main result states that for derived categories of dg modules over a non-positive differential graded ring, every compactly generated localising subcategory is generated by a partial silting object. In particular, every such smashing subcategory admits a silting t-structure.

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Acknowledgements

The authors would like to thank Gustavo Jasso for pointing out examples of non-algebraic triangulated categories satisfying the conditions of our main result, leading to a more general formulation of Theorem 4.5 and to Remark 4.6. The authors acknowledge support from the Program Ricerca di Base 2015 of the University of Verona. Lidia Angeleri Hügel was partly supported by Istituto Nazionale di Alta Matematica INdAM-GNSAGA. Jorge Vitória acknowledges support from the Engineering and Physical Sciences Research Council of the United Kingdom, grant number EP/N016505/1.

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Authors and Affiliations

  1. Dipartimento di Informatica - Settore di Matematica, Università degli Studi di Verona, Strada le Grazie 15 - Ca’ Vignal, 37134, Verona, Italy

    Lidia Angeleri Hügel

  2. Frederik Marks, Institut für Algebra und Zahlentheorie, Universität Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Frederik Marks

  3. Dipartimento di Matematica e Informatica, Università degli Studi di Cagliari, Palazzo delle Scienze, via Ospedale, 72, 09124, Cagliari, Italy

    Jorge Vitória

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  1. Lidia Angeleri Hügel
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  2. Frederik Marks
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  3. Jorge Vitória
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Correspondence to Lidia Angeleri Hügel.

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Angeleri Hügel, L., Marks, F. & Vitória, J. Partial silting objects and smashing subcategories. Math. Z. 296, 887–900 (2020). https://doi.org/10.1007/s00209-019-02450-2

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