2 problems

Let $R$ be a standard bigraded $K$-algebra, let $R_0$ be the $K$-subalgebra generated by the elements of bidegree $(1,0)$, and let $N$ be a finitely generated bigraded $R$-module.…

Let $R$ be a standard bigraded $K$-algebra with irrelevant bigraded ideal $Q$, and let $M$ be a finitely generated bigraded $R$-module. Write $H^k_Q(M)_j$ for the component of seco…