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Homotopical finiteness of smooth and proper dg-algebras

B. Toen
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Abstract

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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B. Toen. 2007-08-02. Homotopical finiteness of smooth and proper dg-algebras. https://arxiv.org/abs/math/0609762

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