#### Vol. 5, No. 4, 2011

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Global descent obstructions for varieties

### Jean-Marc Couveignes and Emmanuel Hallouin

Vol. 5 (2011), No. 4, 431–463
##### Abstract

We show how to transport descent obstructions from the category of covers to the category of varieties. We deduce examples of curves having $Q$ as field of moduli, that admit models over every completion of $Q$, but have no model over $Q$.

##### Keywords
algebraic curve, global field, descent, field of definition, field of moduli, stack
##### Mathematical Subject Classification 2000
Primary: 11R34
Secondary: 12G05, 11G35, 14D22