Derived log stacks after Olsson

Abstract

In this note, we give a formulation of log structures for derived stacks using Olsson's log stack. The derived cotangent complex is then Olsson's logarithmic cotangent complex, which (unlike Gabber's) is just given by log differential forms in the log smooth case. The derived moduli stack of log stable maps then produces the desired virtual tangent space and obstruction theory on the underlying underived stack.