5 problems

Quillen's conjecture. Then $A$ is a quotient of a polynomial ring by an ideal generated by a regular sequence. In other words, $A$ is a complete intersection over $R$. This conject…

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

Herzog's last theorem. The following conditions are equivalent:

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…

Let $f:X\to Y$ be a morphism between quasi-smooth, locally almost of finite presentation derived Artin stacks. Let $L_{X/Y}$ be the relative cotangent complex and let…