Journal title
Compositio Mathematica
DOI
10.1112/S0010437X09004497
Issue
2
Volume
146
Last updated
2024-02-16T19:27:06.007+00:00
Page
271-287
Abstract
We show that a system of r quadratic forms over a -adic field in at least 4r+1 variables will have a non-trivial zero as soon as the cardinality of the residue field is large enough. In contrast, the Ax-Kochen theorem [J. Ax and S. Kochen, Diophantine problems over local fields. I, Amer.J.Math.87 (1965), 605-630] requires the characteristic to be large in terms of the degree of the field over ℚp. The proofs use a p-adic minimization technique, together with counting arguments over the residue class field, based on considerations from algebraic geometry. © 2010 Foundation Compositio Mathematica.
Symplectic ID
53389
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Publication type
Journal Article
Publication date
01 Mar 2010