8 problems

Let $A$ be a graded coherent algebra such that the category $\mathbf{D}^b(\mathsf{qgr}(A))$ admits a classical generator, and let $S$ be the Serre twist functor induced by the grad…

Gromov–Yomdin conjecture. This equality should hold for autoequivalences of the derived category of every smooth projective variety. The result is known in some settings and is for…

Let $\mathcal{C}$ be a saturated $A_{\infty}$-category and let $F$ be an endofunctor of $\mathcal{C}$. The categorical entropy $h_t(F)$ is evaluated at $t=0$ to give $h_0(F)$. Alge…

Let $\mathsf{D}$ be a triangulated category, let $\alpha$ be an exact endofunctor of $\mathsf{D}$, and let $\sigma$ be a fixed stability condition on $\mathsf{D}$. The mass…

Let $X$ be a smooth projective variety over $\mathbb{C}$ and let $D^b(X)$ denote its bounded derived category of coherent sheaves. Let $\mathcal{N}(X)$ be the numerical Grothendiec…

Let $X$ be a smooth projective variety over $\mathbb{C}$, let $\mathrm{D}^b(X)$ be its bounded derived category of coherent sheaves, and let $N(X)$ be its numerical Grothendieck gr…

Let $Y$ be a smooth proper variety over $\mathbb{C}$. Write ${\mathcal D}^b(Y)$ for its bounded derived category of coherent sheaves, and let ${\rm End}^{FM}({\mathcal D}^b(Y))$ de…

Let $X$ be a smooth projective variety, and let ${\rm Auteq}({\mathcal D}^b(X))$ denote the group of isomorphism classes of autoequivalences of ${\mathcal D}^b(X)$. For…