Abstract: Nori proved in 2002 that given a complex algebraic variety $X$, the bounded derived category of the abelian category of constructible sheaves on $X$ is equivalent to the usual triangulated category $D(X)$ of bounded constructible complexes on $X$. He moreover showed that given any constructible sheaf ${\mathcal F}$ on ${\mathbb A}^n$, there is an injection ${\mathcal F}\hookrightarrow {\mathcal G}$ with ${\mathcal G}$ constructible and ${\rm H}^i({\mathbb A}^n, {\mathcal G})=0$ for $i>0$.

In this talk, I'll discuss how to extend Nori's theorem to the case of a variety over an algebraically closed field of positive characteristic, with Betti constructible sheaves replaced by $\ell$-adic sheaves. This is the case $p=0$ of the general problem which asks whether the bounded derived category of $p$-perverse sheaves is equivalent to $D(X)$,resolved affirmatively for the middle perversity by Beilinson.