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The u-invariant of p-adic function fields
Published/Copyright:
March 23, 2012
Abstract
Over a finitely generated field extension in m variables over a p-adic field, any quadratic form in more than 2m + 2 variables has a nontrivial zero. This bound is sharp. We extend this result to a wider class of fields. A key ingredient to our proofs is a recent result of Heath-Brown on systems of quadratic forms over p-adic fields.
Received: 2010-08-31
Revised: 2011-07-05
Published Online: 2012-03-23
Published in Print: 2013-06
©[2013] by Walter de Gruyter Berlin Boston
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- The u-invariant of p-adic function fields
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- The Taylor–Wiles method for coherent cohomology
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Articles in the same Issue
- Classification of surfaces of general type with Euler number 3
- Higher Kronecker “limit” formulas for real quadratic fields
- The u-invariant of p-adic function fields
- The composition Hall algebra of a weighted projective line
- The Taylor–Wiles method for coherent cohomology
- The space of Heegaard splittings
- Wach modules and critical slope p-adic L-functions
- Algebraic varieties with quasi-projective universal cover
- A Lie algebraic approach to Ricci flow invariant curvature conditions and Harnack inequalities
