The derived category of the abelian category of constructible sheaves

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 $\A^n$, there is an injection $\mathcal F\hookrightarrow\mathcal G$ with $\mathcal G$ constructible and $H^i(\A^n,\mathcal G)=0$ 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.

number theory

Audience: researchers in the topic

Comments: pre-talk at 1:30pm

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UCSD number theory seminar

Series comments: Most talks are preceded by a pre-talk for graduate students and postdocs. The pre-talks start 40 minutes prior to the posted time (usually at 1:20pm Pacific) and last about 30 minutes.

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