5 problems

Serre self-duality conjecture. The self-duality induced by the functor $\Theta_{\on{I}(\cG,\cP^-)^{\on{spec,glob}}}$ equals the canonical (Serre) self-duality defined on $\IndCoh$…

Let … be the stack specified in the source. Let $\IndCoh$ denote ind-coherent sheaves and let $D(\Gr_{\GL(n)})^{\operatorname{Hecke}}$ be the Hecke-eigenmodule category on the affi…

Let $X$ be a derived Artin stack, let $B$ be a derived commutative algebra over the de Rham stack $X_{DR}$, and write $X_B=X\mathbin{\times}_{X_{DR}}\operatorname{Spec}(B)$. Let…

Let $X$ and $Y$ be derived stacks, and let $\boldsymbol{\operatorname{IndCoh}}(Y)$ and $\boldsymbol{\operatorname{QCoh}}(Y)$ denote the ind-coherent and quasi-coherent categories o…

Gluing Conjecture. This functor is fully faithful.