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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:

  1. Kato's 3.2 and 3.3 (in http://www.math.brown.edu/~abrmovic/LOGGEOM/Kato-log.pdf) with no f.s. conditions;
  2. locally of finite presentation and with vanishing Gabber relative cotangent complex.
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    $\begingroup$ What is your definition of log etale topology? $\endgroup$ May 5, 2013 at 5:52
  • $\begingroup$ What sort of morphisms do you allow in covers? Strict étale? Kummer étale? $\endgroup$
    – S. Carnahan
    May 5, 2013 at 6:13
  • $\begingroup$ I have edited the question in order to answer Keerthi and Scott. $\endgroup$
    – gabriele
    May 6, 2013 at 18:41

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