All Questions

Let $X$ be a projective algebraic variety over an algebraically closed field. Let an algebraic group $G$ act algebraically on $X$. Let $\mathcal{F}$ be a $G$-equivariant vector bundle (or, more ...

Let $G$ be an affine algebraic group over ${\mathbb C}$. We denote the sheaf of morphisms from ${\mathbb A}^1$ to $G$ by $\bf G$. Then $H^1({\mathbb A}^1,\bf G)=0$ (Cech cohomlogy). Is this fact true? ...