The u-invariant of p-adic function fields

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15 Scopus citations


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.

Original languageEnglish
Pages (from-to)65-73
Number of pages9
JournalJournal fur die Reine und Angewandte Mathematik
Issue number679
StatePublished - Jun 2013

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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