5 problems

Let $F$ be an infinite field and let $n\geq3$. Consider the sequence … … Here $\alpha_1$ and $\alpha_2$ are the two inclusion maps specified in the source. Exactness conjecture. Th…

Let $F$ be an infinite field and let $M_\bullet$ be the exact complex of $\operatorname{GL}_n(F)$-modules used to construct the first-quadrant spectral sequence…

Bass' homology stability conjecture. These maps should be surjective for $n\geq d+i+1$ and bijective for $n\geq d+i+2$.

Characteristic-restriction conjecture. The restrictions on $\operatorname{char}(\mathbb{F})$ in those two theorems are unnecessary.

Sah's homology stability conjecture. This homomorphism should be an isomorphism if $t\geq n+1$ and surjective if $t=n$.