Vol. 5, No. 4, 2011

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editors' Addresses Editors' Interests Scientific Advantages Submission Guidelines Submission Form Editorial Login Author Index To Appear ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print)
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