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Homotopical finiteness of smooth and proper dg-algebras

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arxiv math/0609762 v3 pith:I2XKGMYN submitted 2006-09-27 math.AT math.AG

B. Toen This is my paper · ORCID
classification math.ATmath.AG
keywords propersmoothdg-algebrasintegerbasecertaindeterminedmorphism
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We show that any smooth and proper dg-algebra (over some base ring k) is determined, up to quasi-isomorphism, by its underlying A_n-algebra, for a certain integer n. Similarly, any morphism between two smooth and proper dg-algebras is determined, up to homotopy, by the morphism induced on the underlying A_n-algebras, for a certain integer n. When the base ring k is local, we show that the integer n can be chosen uniformally for all smooth and proper dg-algebras for which two numerical invariants (the "type" and the "cohomogical dimension") are bounded.

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Cited by 1 Pith paper

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  1. Iterated traces in 2-categories and Lefschetz theorems

    math.AT 2019-08 conditional novelty 7.0 of 10

    Iterated traces in any 2-dualizable symmetric monoidal bicategory commute, recovering and extending a wide family of Lefschetz-type theorems.

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