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Semi-Continuity for Derived Categories

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Abstract

We prove that the number of parameters defining a complex of projective modules over an algebra is upper semi-continuous in families of algebras. The proof follows the pattern of the paper by Drozd and Greuel and rests upon universal families with projective bases. Supposing that every algebra is either derived tame or derived wild, we get that a degeneration of a derived wild algebra is also derived wild. We also discuss an apparent counter-example to the last assertion by Th. Brüstle.

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Correspondence to Yuriy A. Drozd.

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16G10, 16E05.

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Drozd, Y.A. Semi-Continuity for Derived Categories. Algebr Represent Theor 8, 239–248 (2005). https://doi.org/10.1007/s10468-005-0967-6

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  • DOI: https://doi.org/10.1007/s10468-005-0967-6

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