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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

A Hasse principle for quadratic forms over function fields


Author: R. Parimala
Journal: Bull. Amer. Math. Soc. 51 (2014), 447-461
Published electronically: March 17, 2014
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Abstract | References | Additional Information

Abstract: We describe the classical Hasse principle for the existence of nontrivial zeros for quadratic forms over number fields, namely, local zeros over all completions at places of the number field imply nontrivial zeros over the number field itself. We then go on to explain more general questions related to the Hasse principle for nontrivial zeros of quadratic forms over function fields, with reference to a set of discrete valuations of the field. This question has interesting consequences over function fields of $ p$-adic curves. We also record some open questions related to the isotropy of quadratic forms over function fields of curves over number fields.


References [Enhancements On Off] (What's this?)

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Additional Information

R. Parimala
Affiliation: Department of Mathematics & Computer Science, Emory University, 400 Dowman Drive NE, Atlanta, Georgia 30322
Email: parimala@mathcs.emory.edu

DOI: http://dx.doi.org/10.1090/S0273-0979-2014-01443-0
PII: S 0273-0979(2014)01443-0
Received by editor(s): August 26, 2013
Received by editor(s) in revised form: October 28, 2013
Published electronically: March 17, 2014
Additional Notes: The author is partially supported by National Science Foundation grant DMS-1001872
(Based on the AWM Noether lectures, delivered at the 2013 AMS-MAA joint meeting at San Diego)
Article copyright: © Copyright 2014 American Mathematical Society