5 problems

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Parimala–Suresh conjecture on the u-invariant of semiglobal fields
Let $K$ be a complete discretely valued field of characteristic zero with perfect residue field $k$ of characteristic $2$ , and let $F$ be the function field of a curve over $K$ . As…
Conjecturesolvedquadratic-forms semiglobal-fields u-invariantarXiv posted 2 days ago
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Pfister's $u$ -invariant conjecture for real fields
Pfister's conjecture.
Conjectureopenquadratic-forms real-algebraic-geometry u-invariantarXiv posted 2 days ago
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The period-index conjecture for the u-invariant of dyadic curve function fields
Period-index conjecture. One has
Conjectureopenquadratic-forms u-invariant valued-fieldsarXiv posted 2 days ago
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The u-invariant bound for function fields over mixed-characteristic complete discretely valued fields
Let $K$ be a complete discretely valued field of characteristic $0$ with residue field $\kappa$ of characteristic $2$ , and let $F$ be the function field of a curve over $K$ . The u-…
Conjectureopenquadratic-forms u-invariant valued-fieldsarXiv posted 2 days ago
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The Laurent-series $u$ -invariant conjecture
Let $k$ be a field and let $F_n=k(\!(t_1,\dotsc,t_n)\!)$ be the Laurent series field in $n$ variables over $k$ , with $n\geq 2$ . For a finite field extension $\ell/k$ , write…
Conjectureopenlaurent-series-fields quadratic-forms u-invariantarXiv posted 2 days ago

Parimala–Suresh conjecture on the u-invariant of semiglobal fields