Logarithmic stacks and minimality

Logarithmic stacks and minimality Article

Gillam, WD. (2012). Logarithmic stacks and minimality . International Journal of Mathematics, 23(7), 10.1142/S0129167X12500693

Given a category fibered in groupoids over schemes with a log structure, one produces a category fibered in groupoids over log schemes. We classify the groupoid fibrations over log schemes that arise in this manner in terms of a categorical notion of "minimal" objects. The classification is actually a purely category-theoretic result about groupoid fibrations over fibered categories, though most of the known applications occur in the setting of log geometry, where our categorical framework encompasses many notions of "minimality" previously extant in the literature. © 2012 World Scientific Publishing Company.