A Quillen model structure of local homotopy equivalences

Abstract

In this note, we construct a closed model structure on the category of Z/2Z-graded complexes of projective systems of ind-Banach spaces. When the base field is the fraction field F of a complete discrete valuation ring V, the homotopy category of this model category is the derived category of Z/2Z -graded complexes of the quasi-abelian category Ind(Ban_F). This homotopy category is the appropriate target of the local and analytic cyclic homology theories for complete, torsionfree V-algebras and F-algebras. When the base field is C, the homotopy category is the target of local and analytic cyclic homology for pro-bornological C-algebras, which includes the subcategory of pro-C*-algebras.