Is it known whether the log étale topology is subcanonical on all, not necessarily fine and saturated, log schemes?
I am interested in the following two possible definitions of log étale between general (i.e. not necessarily fine and saturated) log schemes:
- Kato's 3.2 and 3.3 (in http://www.math.brown.edu/~abrmovic/LOGGEOM/Kato-log.pdf) with no f.s. conditions;
- locally of finite presentation and with vanishing Gabber relative cotangent complex.