3 problems

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. The following are equivalent: $D_s(\Bbb{F}|R)=0$ for $s\gg 0$; $D_s(\Bbb{F}|R)=0$ for $s\geq 3$; and $R$ is a complete intersection. This conjecture character…

Let $\varphi\colon R\to S$ be a ring homomorphism, and let $\operatorname{D}_n(S\!\mid\!R,-)$ denote André–Quillen homology with arbitrary coefficients. Quillen's conjectures. Assu…