So, I've been running in both stacky circles and logarithmic circles and I've been wondering: is there a definition of log stack that is "useful"? I can imagine two such definitions:


1) A log stack is a stack along with an effective divisor (could be useful for studying moduli of smooth curves, then)


2) A log stack is a stack over the category of log schemes


Is either one in standard use? Are they equivalent?



What are Log Stacks
This question was answered in Martin Olsson's thesis ( <http://math.berkeley.edu/~molsson/thesis.ps> ). He gives sufficient conditions for a fibered category on the category of log schemes to arise from "a stack with a log structure", which I think is more or less what Charles intended by Option 1.


