On the Hasse principle for certain quartic hypersurfaces
HTML articles powered by AMS MathViewer
- by Nguyen Ngoc Dong Quan
- Proc. Amer. Math. Soc. 139 (2011), 4293-4305
- DOI: https://doi.org/10.1090/S0002-9939-2011-10936-5
- Published electronically: May 4, 2011
- PDF | Request permission
Abstract:
We prove that there are infinitely many non-isomorphic quartic curves which are counter-examples to the Hasse principle explained by the Brauer-Manin obstruction. Further, these quartic curves have no points defined over number fields of odd degree. As a consequence, we show that there are infinitely many quartic hypersurfaces of arbitrary dimension violating the Hasse principle.References
Bibliographic Information
- Nguyen Ngoc Dong Quan
- Affiliation: Department of Mathematics, The University of Arizona, Tucson, Arizona 85721
- Email: dongquan@math.arizona.edu
- Received by editor(s): November 14, 2009
- Received by editor(s) in revised form: July 5, 2010, and October 26, 2010
- Published electronically: May 4, 2011
- Communicated by: Ken Ono
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 4293-4305
- MSC (2010): Primary 14G05, 11G35, 11G30
- DOI: https://doi.org/10.1090/S0002-9939-2011-10936-5
- MathSciNet review: 2823075
Dedicated: Dedicated to my parents