Rings of definition of smooth and proper dg-algebras

2006/11/17 by Toen, B.
#Algebraic Topology (math.AT) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.math/0611546

Abstract

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.

Related

• Homotopical finiteness of smooth and proper dg-algebras
• Proper connective differential graded algebras and their geometric realizations
• Applications of Differential Graded Algebra Techniques in Commutative Algebra
• A somewhat gentle introduction to differential graded commutative algebra
• Formality of DG algebras (after Kaledin)