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Sums of squares in
algebraic function fields over a complete discretely valued
field
Karim Johannes Becher, David Grimm and Jan Van Geel |
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Vol. 267 (2014), No. 2, 257–276
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Abstract |
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A recently found local-global principle for quadratic forms over function fields of curves over a complete discretely valued field is applied to the study of quadratic forms, sums of squares, and related field invariants. |
Keywords
isotropy, local-global principle, real field, sums of
squares, $u$-invariant, Pythagoras number, valuation,
algebraic function fields
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Mathematical Subject Classification 2010
Primary: 11E04, 11E10, 11E25, 12J10, 14H05
Secondary: 12D15, 12F20
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Milestones
Received: 22 June 2012
Revised: 2 December 2013
Accepted: 6 December 2013
Published: 11 May 2014
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Authors |
| Karim Johannes Becher | |
| Departement Wiskunde en
Informatica Universiteit Antwerpen Middelheimlaan 1 2020 Antwerp Belgium |
Zukunftskolleg Universität Konstanz Box 216 78457 Konstanz Germany |
| David Grimm | |
| École Polytechnique Fédérale de
Lausanne EPFL-SB-MATHGEOM-CSAG Station 8 CH-1015 Lausanne Switzerland |
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| Jan Van Geel | |
| Universiteit Gent Vakgroep Wiskunde Krijgslaan 281 9000 Ghent Belgium |
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