2 problems

Let $X$ be the genus-two curve in characteristic $2$, let $X_1$ be its Frobenius twist, let $F\colon X\to X_1$ be the relative Frobenius morphism, and let $\mathrm{M}_X$ and…

Let $n\in\mathbb N$. Define subcategories of $\mathop{\mathrm D\kern0pt}\nolimits^b(X_n)$ by … with $\mathcal A_0=\langle\mathcal O_{X_n}\rangle$, and for $k<0$ let $\mathcal A_k$…