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In this paper, we investigate properties of the bounded derived category offinite dimensional modules over a gentle or skew-gentle algebra. We show thatthe Rouquier dimension of the derived category of such an algebra is at mostone. Using this result, we prove that the Rouquier dimension of an arbitrarytame projective curve is equal to one, too. Finally, we elaborate theclassification of indecomposable objects of the (possibly unbounded) homotopycategory of projective modules of a gentle algebra.

On the derived categories of gentle and skew-gentle algebras: homological algebra and matrix problems