Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

Stable birational equivalence and geometric Chevalley-Warning


Author: Xia Liao
Journal: Proc. Amer. Math. Soc. 141 (2013), 4049-4055
MSC (2010): Primary 14E08, 14N25, 14Q10
Published electronically: August 2, 2013
MathSciNet review: 3105850
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We propose a ``geometric Chevalley-Warning'' conjecture, that is, a motivic extension of the Chevalley-Warning theorem in number theory. Its statement is equivalent to a recent question raised by F. Brown and O. Schnetz. In this paper we show that the conjecture is true for linear hyperplane arrangements, quadratic and singular cubic hypersurfaces of any dimension, and cubic surfaces in $ \mathbb{P}^3$. The last section is devoted to verifying the conjecture for certain special kinds of hypersurfaces of any dimension. As a by-product, we obtain information on the Grothendieck classes of the affine ``Potts model'' hypersurfaces considered by Aluffi and Marcolli.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 14E08, 14N25, 14Q10

Retrieve articles in all journals with MSC (2010): 14E08, 14N25, 14Q10


Additional Information

Xia Liao
Affiliation: Department of Mathematics, Florida State University, 208 Love Building, 1017 Academic Way, Tallahassee, Florida 32306
Email: xliao@math.fsu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11722-3
Received by editor(s): January 30, 2012
Published electronically: August 2, 2013
Communicated by: Lev Borisov
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.