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Zeros of systems of p-adic quadratic forms

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...

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Publication status:
Published

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Publisher copy:
10.1112/S0010437X09004497

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Journal:
COMPOSITIO MATHEMATICA
Volume:
146
Issue:
2
Pages:
271-287
Publication date:
2010-03-05
DOI:
EISSN:
1570-5846
ISSN:
0010-437X
URN:
uuid:13e7a321-b93a-49e1-8e3e-3079f296cf5e
Source identifiers:
53389
Local pid:
pubs:53389

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