7 problems

CFG conjecture. Every reductive linear algebraic group has property (CFG).

Foley's conjecture. One has

Let $A=(a_{ij})_{n\times n}$ be a Cartan matrix of indefinite type with $n\geq3$, and let $G(A)$ be the associated Kac-Moody group. Infinite-generation conjecture. The rational coh…

Let $W_g=\#^g S^n\times S^n$, let $B\operatorname{Tor}(W_g,D^2)$ be the classifying space of the Torelli group relative to a disc, and let…

Let $k<n$, let $G(k,n)$ be the complex Grassmannian of $k$-planes in $\mathbb{C}^{k+n}$, and let … be its rational cohomology ring. If $h$ is a graded ring endomorphism with…

Let $k$ be a field, let $G$ be a geometrically reductive group or group scheme, and let $A$ be a commutative algebra of finite type with a $G$-action. Write $H^*(G,A)$ for the coho…

A Hamiltonian fibration is a fibration … of closed connected symplectic manifolds. It is rationally cohomologically split when the inclusion of the fiber induces an injective map i…