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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
DOI: https://doi.org/10.1090/S0002-9939-2013-11722-3
Published electronically: August 2, 2013
MathSciNet review: 3105850
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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.


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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: https://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.

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