ScalingStacks

We use the term variety for (not necessarily reduced) quasi-projective separated schemes of finite type over a field $k.$ In the introduction and most of the manuscript $k=\overline{\mathbb{F}}_{p}$ and $G$ is a linear algebraic group over $k.$ For rings $R\subset R^{\prime}$ and $R$-modules $M$ we denote by $M_{R^{\prime}}=M\otimes_{R}R^{\prime}$ the extension of scalars. We use a cohomological convention for chain complexes and denote by $C[n]$ the cohomological shift with $(C[n])^{i}=C^{i+n}.$