6 problems

Let $R$ be a commutative ring and let $S$ be a finitely presented flat commutative $R$-algebra. A commutative ring homomorphism $R\to S$ is very flat when, for every element…

Let $R$ be a ring, let $\mathcal D$ denote the class of all flat Mittag-Leffler $R$-modules, and let $\mathcal D^\perp$ be the class of modules right orthogonal to every module in…

Let $R$ be a commutative ring and let $S_1,\dots,S_m\subset R$ be a finite collection of multiplicative subsets. For $J\subset\{1,\dots,m\}$, let $S_J$ be the multiplicative subset…

Let $R$ be a commutative ring and $S\subset R$ be a multiplicative subset such that the projective dimension of the $R$-module $S^{-1}R$ does not exceed $1$. A flat $R$-module $F$…

Deconstructibility conjecture. The class ${}^\perp(\mathcal{D}_{\mathcal{Q}}^\perp)$ is deconstructible if and only if

Perpendicular-class conjecture. In general,