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Bulletin of the London Mathematical Society Advance Access published online on May 13, 2008
Bulletin of the London Mathematical Society, doi:10.1112/blms/bdn043
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© 2008 London Mathematical Society

Anneaux de définition des dg-algèbres propres et lisses

Bertrand Toën

Laboratoire Emile Picard
Université Paul Sabatier Toulouse 3,
Bat 1R2
31 062 Toulouse cedex 9
France

Received 30 April 2007. Revision received 22 January 2008.

RÈSUMÈ: Soit k = colimi ki une colimite filtrante d’anneaux commutatifs. On montre que la théorie homotopique des dg-algèbres propres et lisses sur k est la colimite des théories homotopiques des dg-algèbres propres et lisses sur les ki. Nous en déduisons en particulier que toute dg-algèbre propre et lisse est définissable sur une Z-algèbre commutative de type fini.

Let k = colimi ki be a filtered colimit of commutative rings. We show 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 the ki. We deduce, in particular, that every smooth and proper dg-algebra can be defined over a commutative Z-algebra of finite type.

2000 Mathematics Subject Classification 16E45.


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