7 problems

Conjecture on the cotangent complex over the field of one element. There exists a functor

Sphere-spectrum duality claim. The result established for coherent, eventually coconnective commutative dg algebras over $\C$ also holds over $\mathbb{S}$: the restricted duality f…

Work over the complete topological $k\llbracket\hbar\rrbracket$-modules, with their symmetric monoidal structure, and let $\mathbbst{BD}_0$ and $\mathbbst{BD}_1$ denote the corresp…

Let $R$ be a Noetherian classical ring, and let $A$ be a $d$-smooth classical $R$-algebra. If the tor-amplitude of $A$ is finite, then it is finite as specified below. Quillen's sm…

For ${\bm{b}}=(b_1,\ldots,b_m)$, let $E_{\bm{b}}$ be the colored polynomial algebra and let $I_{\bm{b}}\vartriangleleft E_{\bm{b}}$ be the colored full-twist ideal. Let…

Let $(A,I)$ be a bounded prism, and let $R$ be a derived $p$-complete simplicial $A/I$-algebra such that $\overline{{\mathlarger{\mathbbl{\Delta}}}}_{R/A}$ is concentrated in degre…

Syzygy conjecture. In particular, the cohomological dimension of the ${\Bbb L}$-module $\Omega^*(X)$ is at most $d$.