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In this paper we consider questions of the following type. Let be a base field and be a field extension. Given a geometric object over a field (e.g. a smooth curve of genus ),
what is the least transcendence degree of a field of definition of over the base field ? In other words, how many independent parameters are needed to define ? To study these questions we
introduce a notion of essential dimension for an algebraic stack. Using the resulting theory, we give a complete answer to...
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