Logarithmic stacks and minimality

Details Logarithmic stacks and minimality Logarithmic stacks and minimality

2011-03-10

arxiv.org/abs/1103.2140v1

Mathematics

Algebraic Geometry

Scientific paper

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.

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