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- W4385849340 abstract "The geometric models for the module category and derived category of any gentle algebra were introduced to realize the objects in module category and derived category by permissible curves and admissible curves respectively. The present paper firstly unifies these two realizations of objects in module category and derived category via same surface for any gentle algebra, by the rotation of permissible curves corresponding to the objects in the module category. Secondly, the geometric characterization of the cohomology of complexes over gentle algebras is established by the truncation of projective permissible curves. It is worth mentioning that the rotation of permissible curves and the truncation of projective permissible curves are mutually inverse processes to some extent. As applications, an alternative proof of ``no gaps theorem as to cohomological length for the bounded derived categories of gentle algebras is provided in terms of the geometric characterization of the cohomology of complexes. Moreover, we obtain a geometric proof for the strong Nakayama conjecture for gentle algebras. Finally, we contain two examples to illustrate our results." @default.
- W4385849340 created "2023-08-16" @default.
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- W4385849340 date "2023-08-14" @default.
- W4385849340 modified "2023-09-27" @default.
- W4385849340 title "Constructing projective resolution and taking cohomology for gentle algebras in the geometric model" @default.
- W4385849340 doi "https://doi.org/10.48550/arxiv.2308.07220" @default.
- W4385849340 hasPublicationYear "2023" @default.
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