Skip to Main Content

Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On abelian birational sections
HTML articles powered by AMS MathViewer

by Hélène Esnault and Olivier Wittenberg
J. Amer. Math. Soc. 23 (2010), 713-724
Published electronically: January 22, 2010


For a smooth and geometrically irreducible variety $X$ over a field $k$, the quotient of the absolute Galois group $G_{k(X)}$ by the commutator subgroup of $G_{\bar k(X)}$ projects onto $G_k$. We investigate the sections of this projection. We show that such sections correspond to “infinite divisions” of the elementary obstruction of Colliot-Thélène and Sansuc. If $k$ is a number field and the Tate–Shafarevich group of the Picard variety of $X$ is finite, then such sections exist if and only if the elementary obstruction vanishes. For curves this condition also amounts to the existence of divisors of degree $1$. Finally we show that the vanishing of the elementary obstruction is not preserved by extensions of scalars.
Similar Articles
Bibliographic Information
  • Hélène Esnault
  • Affiliation: Universität Duisburg–Essen, Mathematik, 45117 Essen, Germany
  • MR Author ID: 64210
  • Email:
  • Olivier Wittenberg
  • Affiliation: Département de mathématiques et applications, École normale supérieure, 45 rue d’Ulm, 75320 Paris Cedex 05, France
  • MR Author ID: 729226
  • Email:
  • Received by editor(s): February 18, 2009
  • Received by editor(s) in revised form: November 28, 2009
  • Published electronically: January 22, 2010
  • Additional Notes: This research was supported in part by the DFG Leibniz Preis, the SFB/TR 45, and the ERC/Advanced Grant 226257
  • © Copyright 2010 by H. Esnault and O. Wittenberg
  • Journal: J. Amer. Math. Soc. 23 (2010), 713-724
  • MSC (2010): Primary 14G32; Secondary 14C25, 14G25, 14G20
  • DOI:
  • MathSciNet review: 2629985