6 problems

An infinite field is a field with infinitely many elements, and an $\mathrm{NIP}$ field is a field whose complete first-order theory has the non-independence property; an $\infty$-…

Tensor-product embedding conjecture. The algebra $\widetilde R$ is $K$-isomorphic to

Let $K$ be an infinite NIP field. NIP-field conjecture. Then $K$ is separably closed, real closed, or admits a non-trivial henselian valuation. This conjecture generalizes the Stab…

Let $F:=\mathbb Q((x_1,\dots,x_n))$ with $n\geq 3$, and let $p(F)$ denote the least integer $r$ such that every sum of squares in $F$ is a sum of at most $r$ squares. Pythagoras-nu…

Let $K$ be a Henselian valued field of characteristic zero with separated analytic structure, and let $A_{m,n}(K)$ denote the ring of separated analytic functions in $m$ variables…

Let $K$ be the quotient field of an excellent, Henselian discrete valuation ring with algebraically closed residue field $k$, and let $X$ be a proper $K$-scheme. Esnault–Levine–Wit…