10 problems

Vasconcelos's differential conjecture. If

Let $F$ be a field and let $\overline{\beta}_{\bullet}(F;n)$ be Cathelineau's additive polylogarithmic complex, placed in degrees $1$ through $n$, with final term…

Let $F$ be an algebraically closed field, and let ${\cal E}_{(n)}^{\ast}(F)$ be the degree-$n$ Euclidean Dehn complex of Euclidean scissor congruence groups. For an $F$-vector spac…

Nonvanishing conjecture. If $A$ is not a principal ideal algebra, equivalently if it has at least one nonprincipal ideal, then

Lenstra's formulation of the Eisenbud–Mazur conjecture. The map induced after tensoring with the residue field $k$ is an isomorphism:

Symbol-length conjecture for differential forms. Then

Let $X$ be an affine or projective curve over a field $\mathbb{k}$ of characteristic zero, let $x$ be a closed point, and let $\widehat{\mathcal{O}_{X,x}}$ denote the completion of…

Vasconcelos' conjecture. Under appropriate separability conditions, finite $\operatorname{projdim}_S \Omega_{S/K}$ should imply that $S$ is a complete intersection.

Let $K$ be the ground field, let $\mathbb W=m_1P_1+\cdots+m_sP_s$ be a fat point scheme in $\mathbb P^n$, and let … Write $R_{\mathbb W}$ for the homogeneous coordinate ring of…

Let $C$ be an algebraically closed extension of infinite transcendence degree of an algebraically closed field $k$ of characteristic $0$, let $G$ be the group of automorphisms of…