9 problems

Let $\fg$ be a Kac–Moody algebra, $\fb$ a Borel subgroup, $\bC$ the curve, and $\mu$ a dominant coweight. Let $\on{Maps}^\mu(\bC,\CG_{\fg,\fb})$ be the corresponding space of maps,…

Let $h:[n]\to[n]$ be a Hessenberg function, let $\mathsf{x}\in\mathfrak{gl}_n(\mathbb{C})$, and let $\varphi_{\mathsf{x},h}$ be the one-parameter family constructed from the associ…

Let $W$ be the affine Weyl group, let $x\in W$, and let $[w,\mathbf{r}]\in\frak{P}$. Let $\calI(x)^+_{w,\mathbf{r}}$ be the corresponding space and let $\frak{c}_{w,\mathbf{r}}$ be…

Formal K-flatness conjecture. Formal K-flatness is equivalent to K-flatness.

Let $k$ be a field, let $\bb V$ and $\bb W$ be $k$-vector spaces with $\dim(\bb W)\leq m$, and let $P:\bb V\to k$ be a polynomial of degree $d$. For an affine map…

Let $A$ be the base ring and let $G\in\operatorname{Gr}^{+}_{A}$ be a group scheme of additive type. Write $G=\operatorname{Spec}(B_G)$ and let $\operatorname{Prim}(B_G)$ denote th…

Non-flatness conjecture. The domain $\operatorname{Int}(D)$ is not flat over $D$ for either of these choices of $D$; in particular, there exists a local, Noetherian, one-dimensiona…

Pappas–Rapoport flatness conjecture. The scheme $P$ is flat over

Vasconcelos's conjecture. $A$ is $R$-flat if and only if its $n$-fold tensor power