AI 中文总结
该研究通过标记带曲面刻画温和代数完美导出范畴的半正交分解，利用曲线旋转诱导函子，在特定条件下得到模范畴的导出分解，为温和代数的导出结构提供了新的刻画方式。
AI 中文摘要
我们通过标记带曲面研究温和代数的完美导出范畴的半正交分解，根据全形式弧系的合适不交并分解来刻画此类分解，并将该描述与对应曲面的良好切割关联起来。对于温和代数，曲线的旋转会诱导出从模范畴的扩张闭子范畴到相关半正交分解分量的完全忠实函子。在额外的阿贝尔性及扩张比较条件下，这些构造给出模范畴的导出分解。
英文摘要
We study semi-orthogonal decompositions of perfect derived categories of gentle algebras via marked ribbon surfaces. We characterize such decompositions in terms of suitable disjoint union decompositions of full formal arc systems, and relate this description to good cuts of the corresponding surfaces. For gentle algebras, rotations of curves induce fully faithful functors from extension-closed subcategories of module categories to the components of the associated semi-orthogonal decompositions. Under additional Abelian and extension-comparison conditions, these constructions give derived decompositions of the module categories.
Comments25 pages, 23 figures
