Anneaux de définition des dg-algèbres propres et lisses.

Bertrand Toen (1)

1 LEP - Laboratoire Émile Picard

This is a companion paper to math.AT/0609762. For a filtered colimit of commutative rings k=colim k_i, we prove that the homotopy theory of smooth and proper dg-algebras over k is the colimit of the homotopy theories of smooth and proper dg-algebras over k_i. As a consequence, we deduce that any smooth and proper dg-algebra can be defined over a commutative Z-algebra of finite type.

Domaines: Topologie algébrique [math.AT]; K-théorie et homologie [math.KT]

Bertrand Toen. Anneaux de définition des dg-algèbres propres et lisses.. Bulletin of the London Mathematical Society, 2007, 40 (4), pp.642-650. ⟨10.1112/blms/bdn043⟩. ⟨hal-00772942⟩