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The generic equivalence among the Lipschitz saturations of a sheaf of modules

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Abstract

In this work, we extend the concept of the Lipschitz saturation of an ideal to the context of modules in some different ways, and we prove they are generically equivalent.

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Acknowledgements

The authors are grateful to Nivaldo Grulha Jr. for his careful reading of this work and to Maria Aparecida Soares Ruas for the valuable conversations about the subject of this work, especially in the generic equivalence among the Lipschitz saturations defined here. The first author was supported in part by PVE-CNPq, grant 401565/2014-9. The second author was supported by Fundação de Amparo à Pesquisa do Estado de São Paulo - FAPESP, Brazil, grant 2013/22411-2. Besides the grants already in the text, the second author also was partially supported by CAPES, grant 88887.909401/2023-00 and grant 88887.897201/2023-00.

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Authors and Affiliations

  1. Department of Mathematics, Northeastern University, 567 Lake Hall, Boston, MA, 02115, USA

    Terence James Gaffney

  2. Department of Mathematics, Federal University of Espírito Santo, Av. Fernando Ferrari, 514 - Goiabeiras, Vitória, ES, 29075-910, Brazil

    Thiago Filipe da Silva

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  1. Terence James Gaffney
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  2. Thiago Filipe da Silva
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Correspondence to Thiago Filipe da Silva.

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Gaffney, T.J., da Silva, T.F. The generic equivalence among the Lipschitz saturations of a sheaf of modules. Res Math Sci 11, 32 (2024). https://doi.org/10.1007/s40687-024-00442-1

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