##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory Seminar

## Owen Barrett

#### University of Chicago

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

Host: Kiran Kedlaya

### April 22, 2021

### 2:00 PM

### Location: See https://www.math.ucsd.edu/\~{}nts/

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