8 problems

Let $G$ be a reductive group, let $^{L}G$ be its Langlands dual, and let $(\chi,w)\in\pi_1(G)\times Z(G)^{\vee}$. Let $\mathbb{T}_{^{L}G}(w)_{-\chi}$ and $\mathbb{T}_G(\chi)_w$ den…

Let $C$ be a smooth projective curve, let $\Omega_C$ be its canonical bundle, and let $B$ be the Hitchin base. For rank $r$, Euler characteristic $\chi$, and weight $w$, write…

Let $C$ be a smooth projective curve of genus $g$, let $L$ be a line bundle on $C$ of degree $l$, and let $g^{\rm{sp}}$ be the genus of the spectral curve. For integers…

Let $d\geqslant 1$, let $w\in\mathbb{Z}$, and let $\mathscr{C}(d)^{\rm{red}}$ be the reduced derived moduli stack of length-$d$ zero-dimensional sheaves on $\mathbb{C}^2$. Let…

Let $S$ be a K3 surface, let $v=dv_0$ with $d\geqslant 1$ and $v_0$ primitive satisfying $\langle v_0,v_0\rangle=0$, and let $S'$ and $\alpha$ be the surface and Brauer class occur…

Let $S$ be a K3 surface, let $v=dv_0$ with $v_0$ primitive and $v_0,v_0=2g-2$, and let $n=\langle v,v\rangle/2+1$. For $w\in\mathbb{Z}$ coprime with $v$, consider the reduced quasi…

K-theoretic computation conjecture.

Schiffmann–Vasserot torsion-freeness conjecture. The $\mathbb{K}$-module $K_T(\mathscr{C}(d))$ is torsion free; consequently, $K_T(\mathbb{T}(d)_v)'$ is isomorphic to…