2 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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Bounded-index conjecture for top cohomology of curve function fields
Let $K$ be a field with $\operatorname{cd}_\ell(K)=n$ , and fix a prime $\ell$ coprime to the characteristic of $K$ . Let $F$ be a function field of a curve over $K$ . The indices of…
Conjecturesolvedgalois-cohomology period-index semiglobal-fieldsarXiv posted 2 days ago

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