8 problems

Let $\varphi\colon R\rightarrow S$ be a homomorphism of commutative rings of finite type, and let $\operatorname{D}_{n}(S|R;-)$ denote the $n$th André–Quillen homology functor on t…

Let $\varphi\colon R\to S$ be a homomorphism of noetherian rings essentially of finite type, and let $\mathcal{L}_{\varphi}$ denote its cotangent complex. Write…

Let $A$ be a simplicial commutative $R$-algebra with finite Noetherian homotopy, and let $\wp\in\operatorname{Spec}(\pi_0A)$ satisfy $\operatorname{char}(k(\wp))>0$. Write…

Let $A$ be a simplicial commutative $R$-algebra with finite Noetherian homotopy, let $\wp\in\operatorname{Spec}(\pi_0A)$ satisfy $\operatorname{char}(k(\wp))>0$, and assume … for…

Let $f:R\to S$ be a homomorphism of Noetherian rings that is essentially of finite type and has finite flat dimension. The homology referred to is André–Quillen homology of $S$ ove…

Quillen's conjecture. If $A$ has finite Noetherian homotopy and $\operatorname{char}(\pi_0 A)\neq 0$, then

Let $\Bbb{F}$ be a field and let $R$ be a simplicial commutative ring that is locally finite and locally of non-zero characteristic. Say that $R$ is locally a complete intersection…

Quillen's conjecture. If $D_i(S|R,-)$ vanishes for all sufficiently large $i$, then it vanishes for every $i\geq 3$.