Model structure on commutative co-Segal dg-algebras in characteristic p>0

Hugo Bacard (1)

1 Department of Mathematics [London, Ontario]

We study weak commutative algebras in a symmetric monoidal model category M. We provide a model structure on these algebras for any symmetric monoidal model category that is combinatorial and left proper. Our motivation was to have a homotopy theory of weak commutative dg-algebras in characteristic p > 0, since there is no such theory for strict commutative dg-algebras. For a general M, we show that if the projective model structure on usual strict commutative algebras exists, then the inclusion from strict to weak algebras is a Quillen equivalence. The results of this paper can be generalized to symmetric co-Segal P-algebras for any operad P. And surprisingly, the axioms of a monoidal model category are not necessary to get the model structure on co-Segal commutative algebras.

Mots clés: dg-algebra; characteristic p; homotopy algebra; co-Segal; commutative dga

Domaines: Topologie algébrique [math.AT]; Algèbre commutative [math.AC]; Catégories et ensembles [math.CT]

Hugo Bacard. Model structure on commutative co-Segal dg-algebras in characteristic p>0. 2014. ⟨hal-00999725⟩