Global descent obstructions for varieties

Jean-Marc Couveignes (1, 2, 3, 4, 5) , Emmanuel Hallouin (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IMB - Institut de Mathématiques de Bordeaux
3 LFANT - Lithe and fast algorithmic number theory
4 UB - Université de Bordeaux
5 CNRS - Centre National de la Recherche Scientifique

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

Domaines: Théorie des nombres [math.NT]; Géométrie algébrique [math.AG]

Jean-Marc Couveignes, Emmanuel Hallouin. Global descent obstructions for varieties. Algebra & Number Theory, 2011, 5 (4), pp.431-463. ⟨10.2140/ant.2011.5.431⟩. ⟨hal-00630393⟩