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Currently displaying 1 – 2 of 2

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A short proof of Rost nilpotence via refined correspondences.

Brosnan, Patrick — 2003

Documenta Mathematica

Essential dimension of moduli of curves and other algebraic stacks

Patrick Brosnan; Zinovy Reichstein; Angelo Vistoli — 2011

Journal of the European Mathematical Society

In this paper we consider questions of the following type. Let $k$ be a base field and $K / k$ be a field extension. Given a geometric object $X$ over a field $K$ (e.g. a smooth curve of genus $g$ ), what is the least transcendence degree of a field of definition of $X$ over the base field $k$ ? In other words, how many independent parameters are needed to define $X$ ? 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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